The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was...The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was discussed in this study.To efficiently and accurately compute the exponential of the dynamics state matrix and the matrix functions due to external loads,an adaptively filtered precise integration method was proposed,which inherits the high precision of the precise integrationmethod,improves the computational efficiency and saves the memory required.Moreover,the perturbation method was introduced to avoid repeated computations of matrix exponential and terms due to external loads.Based on the filtering and perturbation techniques,an adaptively filtered precise integration method considering perturbation for stochastic dynamics problems was developed.Two numerical experiments,including a model of phononic crystal and a bridge model considering random parameters,were performed to test the performance of the proposed method in terms of accuracy and efficiency.Numerical results show that the accuracy and efficiency of the proposed method are better than those of the existing precise integration method,the Newmark-βmethod and the Wilson-θmethod.展开更多
With the rapid increase of observational,experimental and simulated data for stochastic systems,tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems.Despite the ...With the rapid increase of observational,experimental and simulated data for stochastic systems,tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems.Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena,the data-driven approaches to extracting stochastic dynamics with Levy noise are relatively few.In this work,we propose aWeak Collocation Regression(WCR)to explicitly reveal unknown stochastic dynamical systems,i.e.,the Stochastic Differential Equation(SDE)with bothα-stable Levy noise and Gaussian noise,from discrete aggregate data.This method utilizes the evolution equation of the probability distribution function,i.e.,the Fokker-Planck(FP)equation.With the weak form of the FP equation,the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations.Then,the unknown parameters are obtained by a sparse linear regression.For a SDE with Levy noise,the corresponding FP equation is a partial integro-differential equation(PIDE),which contains nonlocal terms,and is difficult to deal with.The weak form can avoid complicated multiple integrals.Our approach can simultaneously distinguish mixed noise types,even in multi-dimensional problems.Numerical experiments demonstrate that our method is accurate and computationally efficient.展开更多
The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral(WPI)technique.The system can be construed as a representative model...The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral(WPI)technique.The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators,and relates to an experiment performed by Buks and Roukes.Compared to alternative modeling and solution treatments in the literature,the paper exhibits the following novelties.First,typically adopted linear,or higher‐order polynomial,approximations of the nonlinear electrostatic forces are circumvented.Second,for the first time,stochastic modeling is employed by considering a random excitation component representing the effect of diverse noise sources on the system dynamics.Third,the resulting high‐dimensional,nonlinear system of coupled stochastic differential equations governing the dynamics of the micromechanical array is solved based on the WPI technique for determining the response joint probability density function.Comparisons with pertinent Monte Carlo simulation data demonstrate a quite high degree of accuracy and computational efficiency exhibited by the WPI technique.Further,it is shown that the proposed model can capture,at least in a qualitative manner,the salient aspects of the frequency domain response of the associated experimental setup.展开更多
We introduce a lattice-free hard sphere exclusion stochastic process.The resulting stochastic rates are distance based instead of cell based.The corresponding Markov chain build for this many particle system is update...We introduce a lattice-free hard sphere exclusion stochastic process.The resulting stochastic rates are distance based instead of cell based.The corresponding Markov chain build for this many particle system is updated using an adaptation of the kinetic Monte Carlo method.It becomes quickly apparent that due to the latticefree environment,and because of that alone,the dynamics behave differently than those in the lattice-based environment.This difference becomes increasingly larger with respect to particle densities/temperatures.Thewell-known packing problemand its solution(Palasti conjecture)seem to validate the resulting lattice-free dynamics.展开更多
Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems.In this paper,a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Ga...Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems.In this paper,a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example.Noise‐induced phenomena,such as noise‐induced quasi‐cycle,three‐state intermittency,and chaos,are observed.In the intermittency process,the optimal path used to describe the transition mechanism is calculated and confirmed to pass through an unstable periodic orbit,a chaotic saddle,a saddle point,and a heteroclinic trajectory in an orderly sequence using generalized cell mapping with a digraph method constructively.The corresponding optimal fluctuation forces are delineated to uncover the effects of noise during the transition process.Then the process will switch frequently between the attractors and the chaotic saddle as noise intensity increased further,that is,noise induced chaos emerging.A threshold noise intensity is defined by stochastic sensitivity analysis when a confidence ellipsoid is tangent to the stable manifold of the periodic orbit,which agrees with the simulation results.It is finally reported that these results and methods can be generalized to analyze the stochastic dynamics of other nonlinear mechanical systems with similar structures.展开更多
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics...The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.展开更多
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statisti...The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.展开更多
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic...This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.展开更多
Based on recent work, I will give a nontechnical brief review of a powerful quantitative concept in biology, adaptive landscape, ini- tially proposed by S. Wright over 70 years ago, reintroduced by one of the founders...Based on recent work, I will give a nontechnical brief review of a powerful quantitative concept in biology, adaptive landscape, ini- tially proposed by S. Wright over 70 years ago, reintroduced by one of the founders of molecular biology and by others in different bio- logical contexts, but apparently forgotten by modem biologists for many years. Nevertheless, this concept finds an increasingly important role in the development of systems biology and bionetwork dynamics modeling, from phage lambda genetic switch to endogenous net- work for cancer genesis and progression. It is an ideal quantification to describe the robustness and stability of bionetworks. Here, I will first introduce five landmark proposals in biology on this concept, to demonstrate an important common thread in theoretical biology. Then I will discuss a few recent results, focusing on the studies showing theoretical consistency of adaptive landscape. From the perspec- tive of a working scientist and of what is needed logically for a dynamical theory when confronting empirical data, the adaptive landscape is useful both metaphorically and quantitatively, and has captured an essential aspect of biological dynamical processes. Though at the theoretical level the adaptive landscape must exist and it can be used across hierarchical boundaries in biology, many associated issues are indeed vague in their initial formulations and their quantitative realizations are not easy, and are good research topics for quantitative biologists. I will discuss three types of open problems associated with the adaptive landscape in a broader perspective.展开更多
In a global dynamic analysis,the coexisting attractors and their basins are the main tools to understand the system behavior and safety.However,both basins and attractors can be drastically influenced by uncertainties...In a global dynamic analysis,the coexisting attractors and their basins are the main tools to understand the system behavior and safety.However,both basins and attractors can be drastically influenced by uncertainties.The aim of this work is to illustrate a methodology for the global dynamic analysis of nondeterministic dynamical systems with competing attractors.Accordingly,analytical and numerical tools for calculation of nondeterministic global structures,namely attractors and basins,are proposed.First,based on the definition of the Perron-Frobenius,Koopman and Foias linear operators,a global dynamic description through phase-space operators is presented for both deterministic and nondeterministic cases.In this context,the stochastic basins of attraction and attractors’distributions replace the usual basin and attractor concepts.Then,numerical implementation of these concepts is accomplished via an adaptative phase-space discretization strategy based on the classical Ulam method.Sample results of the methodology are presented for a canonical dynamical system.展开更多
The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature.While many such applications utilize frequency or time domain formulations,relatively few con...The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature.While many such applications utilize frequency or time domain formulations,relatively few consider stochastic dynamic excitations.This paper presents an efficient and compact code called TopSTO for structural topology optimization considering stationary stochastic dynamic loading using a method derived from random vibration theory.The theory,described in conjunction with the implementation in the provided code,is illustrated for a seismically excited building.This work demonstrates the efficiency of the approach in terms of both the computational resources and minimal amount of code required.This code is intended to serve as a baseline for understanding the theory and implementation of this topology optimization approach and as a foundation for additional applications and developments.展开更多
A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic be- havior of an MR damper is characterized by the ...A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic be- havior of an MR damper is characterized by the Bouc-Wen hysteretic model. The control force produced by the MR damper is separated into a passive part incorporated in the uncontrolled system and a semi-active part to be determined. The system combining the Bouc-Wen hysteretic force is converted into an equivalent non-hysteretic nonlinear stochastic control system. Then It?o stochastic di?erential equations are derived from the equivalent system by using the stochastic averaging method. A dynamical programming equation for the controlled di?usion processes is established based on the stochastic dynamical programming principle. The non-clipping nonlin- ear optimal control law is obtained for a certain performance index by minimizing the dynamical programming equation. Finally, an example is given to illustrate the application and e?ectiveness of the proposed control strategy.展开更多
The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabil...The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.展开更多
This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequal...This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given s...We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.展开更多
Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression b...Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.展开更多
Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic ...Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic dynamic modeling(SDM) is considered as an effective way to predict real-time satellite channel fading caused by rain. This article carries out a survey of SDM using stochastic differential equations(SDEs) currently in the literature. Special attention is given to the different input characteristics of each model to satisfy specific local conditions. Future research directions in SDM are also suggested in this paper.展开更多
This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density fun...This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.展开更多
This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed...This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed adaptive controller and the update of the control gain designed in this paper all happen randomly. Based on the Lyapunov stability theory, LaSalle invariance principle, combined with the use of the properties of the matrix Kronecker product, stochastic differential equation theory and other related tools, by constructing the appropriate Lyapunov functional, the criterion for the distributed synchronization of this type of stochastic complex networks in mean square is obtained.展开更多
基金the support of the National Natural Science Foundation of China(Grant Nos.11472067 and 51609034)the Science Foundation of Liaoning Province of China(No.2021-MS-119)+1 种基金the Dalian Youth Science and Technology Star Project(No.2018RQ06)the Fundamental Research Funds for the Central Universities(Grant No.DUT20GJ216).
文摘The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was discussed in this study.To efficiently and accurately compute the exponential of the dynamics state matrix and the matrix functions due to external loads,an adaptively filtered precise integration method was proposed,which inherits the high precision of the precise integrationmethod,improves the computational efficiency and saves the memory required.Moreover,the perturbation method was introduced to avoid repeated computations of matrix exponential and terms due to external loads.Based on the filtering and perturbation techniques,an adaptively filtered precise integration method considering perturbation for stochastic dynamics problems was developed.Two numerical experiments,including a model of phononic crystal and a bridge model considering random parameters,were performed to test the performance of the proposed method in terms of accuracy and efficiency.Numerical results show that the accuracy and efficiency of the proposed method are better than those of the existing precise integration method,the Newmark-βmethod and the Wilson-θmethod.
基金supported by the National Key R&D Program of China(Grant No.2021YFA0719200).
文摘With the rapid increase of observational,experimental and simulated data for stochastic systems,tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems.Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena,the data-driven approaches to extracting stochastic dynamics with Levy noise are relatively few.In this work,we propose aWeak Collocation Regression(WCR)to explicitly reveal unknown stochastic dynamical systems,i.e.,the Stochastic Differential Equation(SDE)with bothα-stable Levy noise and Gaussian noise,from discrete aggregate data.This method utilizes the evolution equation of the probability distribution function,i.e.,the Fokker-Planck(FP)equation.With the weak form of the FP equation,the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations.Then,the unknown parameters are obtained by a sparse linear regression.For a SDE with Levy noise,the corresponding FP equation is a partial integro-differential equation(PIDE),which contains nonlocal terms,and is difficult to deal with.The weak form can avoid complicated multiple integrals.Our approach can simultaneously distinguish mixed noise types,even in multi-dimensional problems.Numerical experiments demonstrate that our method is accurate and computationally efficient.
文摘The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral(WPI)technique.The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators,and relates to an experiment performed by Buks and Roukes.Compared to alternative modeling and solution treatments in the literature,the paper exhibits the following novelties.First,typically adopted linear,or higher‐order polynomial,approximations of the nonlinear electrostatic forces are circumvented.Second,for the first time,stochastic modeling is employed by considering a random excitation component representing the effect of diverse noise sources on the system dynamics.Third,the resulting high‐dimensional,nonlinear system of coupled stochastic differential equations governing the dynamics of the micromechanical array is solved based on the WPI technique for determining the response joint probability density function.Comparisons with pertinent Monte Carlo simulation data demonstrate a quite high degree of accuracy and computational efficiency exhibited by the WPI technique.Further,it is shown that the proposed model can capture,at least in a qualitative manner,the salient aspects of the frequency domain response of the associated experimental setup.
文摘We introduce a lattice-free hard sphere exclusion stochastic process.The resulting stochastic rates are distance based instead of cell based.The corresponding Markov chain build for this many particle system is updated using an adaptation of the kinetic Monte Carlo method.It becomes quickly apparent that due to the latticefree environment,and because of that alone,the dynamics behave differently than those in the lattice-based environment.This difference becomes increasingly larger with respect to particle densities/temperatures.Thewell-known packing problemand its solution(Palasti conjecture)seem to validate the resulting lattice-free dynamics.
基金Six Talent Peaks Project in Jiangsu Province,China,Grant/Award Number:JXQC‐002。
文摘Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems.In this paper,a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example.Noise‐induced phenomena,such as noise‐induced quasi‐cycle,three‐state intermittency,and chaos,are observed.In the intermittency process,the optimal path used to describe the transition mechanism is calculated and confirmed to pass through an unstable periodic orbit,a chaotic saddle,a saddle point,and a heteroclinic trajectory in an orderly sequence using generalized cell mapping with a digraph method constructively.The corresponding optimal fluctuation forces are delineated to uncover the effects of noise during the transition process.Then the process will switch frequently between the attractors and the chaotic saddle as noise intensity increased further,that is,noise induced chaos emerging.A threshold noise intensity is defined by stochastic sensitivity analysis when a confidence ellipsoid is tangent to the stable manifold of the periodic orbit,which agrees with the simulation results.It is finally reported that these results and methods can be generalized to analyze the stochastic dynamics of other nonlinear mechanical systems with similar structures.
基金The project supported in part by USA NIH Grant under HG002894
文摘The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
基金Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11125419)the National Natural Science Foundation of China(Grant No.10925525)+1 种基金the Funds for the Leading Talents of Fujian ProvinceChina
文摘The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.
基金supported by National Natural Science Foundation of China (No. 60774010, 10971256, and 60974028)Jiangsu"Six Top Talents" (No. 07-A-020)+2 种基金Natural Science Foundation of Jiangsu Province (No. BK2009083)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.07KJB510114)Natural Science Foundation of Xuzhou Normal University (No. 08XLB20)
文摘This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
基金supported in part by a grant from USA National Institutes of Health (No. K25-HG002894-05)985 Project from Shanghai Jiao Tong University.
文摘Based on recent work, I will give a nontechnical brief review of a powerful quantitative concept in biology, adaptive landscape, ini- tially proposed by S. Wright over 70 years ago, reintroduced by one of the founders of molecular biology and by others in different bio- logical contexts, but apparently forgotten by modem biologists for many years. Nevertheless, this concept finds an increasingly important role in the development of systems biology and bionetwork dynamics modeling, from phage lambda genetic switch to endogenous net- work for cancer genesis and progression. It is an ideal quantification to describe the robustness and stability of bionetworks. Here, I will first introduce five landmark proposals in biology on this concept, to demonstrate an important common thread in theoretical biology. Then I will discuss a few recent results, focusing on the studies showing theoretical consistency of adaptive landscape. From the perspec- tive of a working scientist and of what is needed logically for a dynamical theory when confronting empirical data, the adaptive landscape is useful both metaphorically and quantitatively, and has captured an essential aspect of biological dynamical processes. Though at the theoretical level the adaptive landscape must exist and it can be used across hierarchical boundaries in biology, many associated issues are indeed vague in their initial formulations and their quantitative realizations are not easy, and are good research topics for quantitative biologists. I will discuss three types of open problems associated with the adaptive landscape in a broader perspective.
基金support of the Brazil-ian research agencies,the National Council for Scientific and Technological Development (CNPq)(Nos. 301355/2018-5 and 200198/2022-0)FAPERJ-CNE (No. E-26/202.711/2018)+1 种基金FAPERJ Nota 10 (No. E-26/200.357/2020)CAPES (Finance code 001 and 88881.310620/2018-01)。
文摘In a global dynamic analysis,the coexisting attractors and their basins are the main tools to understand the system behavior and safety.However,both basins and attractors can be drastically influenced by uncertainties.The aim of this work is to illustrate a methodology for the global dynamic analysis of nondeterministic dynamical systems with competing attractors.Accordingly,analytical and numerical tools for calculation of nondeterministic global structures,namely attractors and basins,are proposed.First,based on the definition of the Perron-Frobenius,Koopman and Foias linear operators,a global dynamic description through phase-space operators is presented for both deterministic and nondeterministic cases.In this context,the stochastic basins of attraction and attractors’distributions replace the usual basin and attractor concepts.Then,numerical implementation of these concepts is accomplished via an adaptative phase-space discretization strategy based on the classical Ulam method.Sample results of the methodology are presented for a canonical dynamical system.
文摘The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature.While many such applications utilize frequency or time domain formulations,relatively few consider stochastic dynamic excitations.This paper presents an efficient and compact code called TopSTO for structural topology optimization considering stationary stochastic dynamic loading using a method derived from random vibration theory.The theory,described in conjunction with the implementation in the provided code,is illustrated for a seismically excited building.This work demonstrates the efficiency of the approach in terms of both the computational resources and minimal amount of code required.This code is intended to serve as a baseline for understanding the theory and implementation of this topology optimization approach and as a foundation for additional applications and developments.
基金Project supported by the Zhejiang Provincial Natural Sciences Foundation (No. 101046) and the foundation fromHong Kong RGC (No. PolyU 5051/02E).
文摘A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic be- havior of an MR damper is characterized by the Bouc-Wen hysteretic model. The control force produced by the MR damper is separated into a passive part incorporated in the uncontrolled system and a semi-active part to be determined. The system combining the Bouc-Wen hysteretic force is converted into an equivalent non-hysteretic nonlinear stochastic control system. Then It?o stochastic di?erential equations are derived from the equivalent system by using the stochastic averaging method. A dynamical programming equation for the controlled di?usion processes is established based on the stochastic dynamical programming principle. The non-clipping nonlin- ear optimal control law is obtained for a certain performance index by minimizing the dynamical programming equation. Finally, an example is given to illustrate the application and e?ectiveness of the proposed control strategy.
基金supported by the National Natural Science Foundation of China(607404306646087403160904060)
文摘The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.
基金supported by the National Natural Science Foundation of China (Grant No.60974139)the Fundamental Research Funds for the Central Universities (Grant No.72103676)
文摘This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
基金supported by the National Natural Science Foundation of China (11172260 and 11072213)the Fundamental Research Fund for the Central University of China (2011QNA4001)
文摘We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.
基金Federal Highway Administration Under Grant No. DDEGRD-06-X-00408
文摘Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.
基金supported by the National Natural Science Foundation of China (Grant No.91338201)
文摘Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic dynamic modeling(SDM) is considered as an effective way to predict real-time satellite channel fading caused by rain. This article carries out a survey of SDM using stochastic differential equations(SDEs) currently in the literature. Special attention is given to the different input characteristics of each model to satisfy specific local conditions. Future research directions in SDM are also suggested in this paper.
文摘This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.
文摘This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed adaptive controller and the update of the control gain designed in this paper all happen randomly. Based on the Lyapunov stability theory, LaSalle invariance principle, combined with the use of the properties of the matrix Kronecker product, stochastic differential equation theory and other related tools, by constructing the appropriate Lyapunov functional, the criterion for the distributed synchronization of this type of stochastic complex networks in mean square is obtained.
