In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic （DHSP） solit...In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic （DHSP） solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.展开更多
In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating so...In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating soliton and fronts can be realised through a series of period-doubling bifurcations, while there exist many kinds of special solutions. The complete transformation diagram has been obtained when the value of nonlinear gain varies within a definite range. The detailed analysis of the diagram reveals that the pulsating soliton experiences period-doubling bifurcations for smaller values of the nonlinear gain. For larger values of it, the pulsating solitons show chaotic behaviour and complex pulse splitting except for some special bifurcations. With the value of nonlinear gain increasing further, the pulse profiles resume pulsating, but the pulse energy are much higher than before and the pulse centre may move along the propagation direction.展开更多
The complex cubic-quintic Ginzburg-Landau equation(CQGLE)is a universal model for describing a dissipative system,especially fiber laser.The analytic one-soliton solution of the variable-coefficients CQGLE is calculat...The complex cubic-quintic Ginzburg-Landau equation(CQGLE)is a universal model for describing a dissipative system,especially fiber laser.The analytic one-soliton solution of the variable-coefficients CQGLE is calculated by a modified Hirota method.Then,phenomena of soliton pulses splitting and stable bound states of two solitons are investigated.Moreover,rectangular dissipative soliton pulses of the variable-coefficients CQGLE are realized and controlled effectively in the theoretical research for the first time,which breaks through energy limitation of soliton pulses and is expected to provide theoretical basis for preparation of high-energy soliton pulses in fiber lasers.展开更多
For a typical dissipative system,a driven harmonic oscillator put in a heat bath,we obtain a simple and exact solution for the reduced density operator of the system,which gives the result obtained by the master equat...For a typical dissipative system,a driven harmonic oscillator put in a heat bath,we obtain a simple and exact solution for the reduced density operator of the system,which gives the result obtained by the master equation approach under the small damping approximation.This method gives a simple way to get exact solutions of many problems about dissipative systems in quantum optics.展开更多
This paper dwells upon the asymptotic behavior, as t→∞, of the integral solution u(t) to the nonhaear evolution equation u'(t) ∈A(t)u(f) + g(t),t≥s,u(s) =xo∈D(A(a)),where {A(t)}t≥s is a family m-ipative oper...This paper dwells upon the asymptotic behavior, as t→∞, of the integral solution u(t) to the nonhaear evolution equation u'(t) ∈A(t)u(f) + g(t),t≥s,u(s) =xo∈D(A(a)),where {A(t)}t≥s is a family m-ipative operator in a Hlilbert space H,and g∈L(loc)(0,∞;H). We prove that converges weakly, as t→∞, uniforluly in h≥0, which applies that u(t) is weak convergence if and only if u(t) is weakly asymptotically regular i.e., u(t + h) -u(f) →0 for h≥0.展开更多
A simple and general theory to describe basic irreversible thermodynamic aspects of aging in all dissipative living is presented. Any dissipative system during its operation continuously loses efficiency by the produc...A simple and general theory to describe basic irreversible thermodynamic aspects of aging in all dissipative living is presented. Any dissipative system during its operation continuously loses efficiency by the production of structural or functional defects because of the second law of thermodynamics. This continuous loss of efficiency occurs on all the dissipative systems through the realization of specific functional cycles, leading to a maximum action principle of any system involving the Planck’s constant during their total dissipative operation. We applied our theory to the calculation of men and women lifespans from basal metabolic rate per unit weight and to the calculation of a new aging parameter per cycle of some human organs or physiological functions. All microscopic theory of the aging of living beings should be consistent with the second law of the thermodynamics. In other words, the operation of the biological self-organized structures only implies a delay in which the dissipative biological systems outside of equilibrium approach inexorably to the thermodynamic equilibrium obeying the second law of the thermodynamics.展开更多
We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, givi...We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, giving the evolution of the light pulses parameters as a function of the propagation distance. The collective variables approach permits us to obtain, efficiently, a global mapping of the 3D stationary dissipative solitons. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Thus it helps to show the impact of dispersion and nonlinear gain on the stationary dynamic.展开更多
In this study,a novel observer-based scalable control scheme for large-scale systems(LSSs)with several interconnected subsystems is explored.Firstly,a scalable observer-based controller is designed to address complex ...In this study,a novel observer-based scalable control scheme for large-scale systems(LSSs)with several interconnected subsystems is explored.Firstly,a scalable observer-based controller is designed to address complex situations where system states are difficult to measure directly.Secondly,unlike the limited cascade and ring topology connections in previous results,this study considers a universal arbitrary topology.Furthermore,it is noteworthy that the plug-and-play(PnP)capability of LSSs is guaranteed thanks to the proposed scalable scheme.Specifically,when subsystems are added or removed,only the controller gains of directly connected neighbors need updating,eliminating the need to redesign the entire system.Moreover,by choosing a Lyapunov-Krasovskii function with a quadratic matrix-valued polynomial,sufficient conditions are deduced to guarantee the global exponential stability with the desired extended dissipative performance for the resulting LSSs.Finally,the effectiveness of the employed scheme is verified by numerical and microgrid examples.展开更多
From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretica...From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.展开更多
By combining all optical,electronic,and mechanical capabilities,electro-optomechanical systems,along with the use of mechanical displacement,the conversion of low-frequency electrical signals into much higher-frequenc...By combining all optical,electronic,and mechanical capabilities,electro-optomechanical systems,along with the use of mechanical displacement,the conversion of low-frequency electrical signals into much higher-frequency optical signals is possible.This process provides several capabilities that have very important applications in various fields,including classical,as well as quantum communications.In this regard,the inevitable effect of dissipation on the performance indicators of such systems is one of the important issues affecting its efficiency.One approach for investigating the effect of dissipation is based on a time-dependent Hamiltonian has been known as the Caldirola-Kanai(CK)Hamiltonian,wherein the exponentially increasing mass,i.e.m(t)=m0(eγt)enters the mechanical oscillator system.Utilizing this approach shows that,the performance of the system under the influence of dissipation with CK Hamiltonian formalism,in which the dissipation terms are embedded in the Hamiltonian,are more logical,analytical,and reliable than considering the effect of dissipation with the phenomenological method(including the dissipation effects in the equations of motion by hand),which has been recently used in Bagci et al.(Nature,507,81,2014).In our method,it is also possible to monitor the performance of the system via the adjustment of dissipation components,i.e.,resistance R and reactance L(and CK damping parameterγ)in the electrical(mechanical membrane)part of the system.展开更多
More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtain...More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.展开更多
This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These model...This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These models offer valuable insights into nonlinear wave propagation,with applications in fluid dynamics and materials science,including systems such as liquid crystals and ferrofluids.It is shown that the conservative Sawada-Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles,as well as two-and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation(ODE)system.For the dissipative generalized Sawada-Kotera equation,chaotic wave behavior is observed.The transition to chaos in the corresponding ODE systemfollows a universal bifurcation scenario consistent with the framework established by FShM(Feigenbaum-Sharkovsky-Magnitskii)theory.Notably,this study demonstrates for the first time that the conservative Sawada-Kotera equation can exhibit complex quasi-periodic wave solutions,while its dissipative counterpart admits an infinite number of stable periodic and chaotic waveforms.展开更多
This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx＋（ζθ）x＋aθxx,ζt=-θ...This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx＋（ζθ）x＋aθxx,ζt=-θx＋βζxx;with initial data and end states （ζθ）（x,0）=（ζ0,θ0）（x）→（ζ±,θ±）as x→∞.We obtain the existence of traveling wave solutions by phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without restrictions on the coeffi- cients a and v by the method of energy estimates.展开更多
This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with t...This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.展开更多
This article is concerned with the problem of robust dissipative filtering for continuous-time polytopic uncertain neutral systems. The main purpose is to obtain a stable and proper linear filter such that the filteri...This article is concerned with the problem of robust dissipative filtering for continuous-time polytopic uncertain neutral systems. The main purpose is to obtain a stable and proper linear filter such that the filtering error system is strictly dissipative. A new criterion for the dissipativity of neutral systems is first provided in terms of linear matrix inequalities （LMI）. Then, an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems. Two numerical examples are given. One illustrates the less conservativeness of the proposed criterion; the other demonstrates the validity of the filtering design procedure.展开更多
The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on...The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.展开更多
By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipat...By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.展开更多
In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term an...In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term and its coefficient are suitably chosen, this scheme possesses discrete homoclinic orbits, which approximate the continuous homoclinic orbits with second order accuracy w.r. to time-step size.展开更多
This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special...This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special cases. The paper is concerned with the design of dissipative static state feedback controllers such that the closed-loop system is (robustly) asymptotically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative state feedback controllers are obtained by using a linear matrix inequality (LMI) approach. It is shown that the solvability of dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H ∞ control and passive control.展开更多
The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory.We in...The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory.We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment.Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla.Particularly,via preparing the state of the system to the highest excited state with hight fidelity,the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously.We explain these results using the definition of state fidelity.Furthermore,we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control.Therefore,our results may be of importance in the context of quantum information technologies.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10574051 and 10174025)
文摘In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic （DHSP） solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.
文摘In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating soliton and fronts can be realised through a series of period-doubling bifurcations, while there exist many kinds of special solutions. The complete transformation diagram has been obtained when the value of nonlinear gain varies within a definite range. The detailed analysis of the diagram reveals that the pulsating soliton experiences period-doubling bifurcations for smaller values of the nonlinear gain. For larger values of it, the pulsating solitons show chaotic behaviour and complex pulse splitting except for some special bifurcations. With the value of nonlinear gain increasing further, the pulse profiles resume pulsating, but the pulse energy are much higher than before and the pulse centre may move along the propagation direction.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11875008 and 12075034)the Beijing University of Posts and Telecommunications Excellent Ph.D.Students Foundation(Grant No.CX2021129)。
文摘The complex cubic-quintic Ginzburg-Landau equation(CQGLE)is a universal model for describing a dissipative system,especially fiber laser.The analytic one-soliton solution of the variable-coefficients CQGLE is calculated by a modified Hirota method.Then,phenomena of soliton pulses splitting and stable bound states of two solitons are investigated.Moreover,rectangular dissipative soliton pulses of the variable-coefficients CQGLE are realized and controlled effectively in the theoretical research for the first time,which breaks through energy limitation of soliton pulses and is expected to provide theoretical basis for preparation of high-energy soliton pulses in fiber lasers.
基金Supported by the National Natural Science Foundation of China.
文摘For a typical dissipative system,a driven harmonic oscillator put in a heat bath,we obtain a simple and exact solution for the reduced density operator of the system,which gives the result obtained by the master equation approach under the small damping approximation.This method gives a simple way to get exact solutions of many problems about dissipative systems in quantum optics.
文摘This paper dwells upon the asymptotic behavior, as t→∞, of the integral solution u(t) to the nonhaear evolution equation u'(t) ∈A(t)u(f) + g(t),t≥s,u(s) =xo∈D(A(a)),where {A(t)}t≥s is a family m-ipative operator in a Hlilbert space H,and g∈L(loc)(0,∞;H). We prove that converges weakly, as t→∞, uniforluly in h≥0, which applies that u(t) is weak convergence if and only if u(t) is weakly asymptotically regular i.e., u(t + h) -u(f) →0 for h≥0.
文摘A simple and general theory to describe basic irreversible thermodynamic aspects of aging in all dissipative living is presented. Any dissipative system during its operation continuously loses efficiency by the production of structural or functional defects because of the second law of thermodynamics. This continuous loss of efficiency occurs on all the dissipative systems through the realization of specific functional cycles, leading to a maximum action principle of any system involving the Planck’s constant during their total dissipative operation. We applied our theory to the calculation of men and women lifespans from basal metabolic rate per unit weight and to the calculation of a new aging parameter per cycle of some human organs or physiological functions. All microscopic theory of the aging of living beings should be consistent with the second law of the thermodynamics. In other words, the operation of the biological self-organized structures only implies a delay in which the dissipative biological systems outside of equilibrium approach inexorably to the thermodynamic equilibrium obeying the second law of the thermodynamics.
文摘We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, giving the evolution of the light pulses parameters as a function of the propagation distance. The collective variables approach permits us to obtain, efficiently, a global mapping of the 3D stationary dissipative solitons. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Thus it helps to show the impact of dispersion and nonlinear gain on the stationary dynamic.
基金supported in part by the National Natural Science Foundation of China(62173218).
文摘In this study,a novel observer-based scalable control scheme for large-scale systems(LSSs)with several interconnected subsystems is explored.Firstly,a scalable observer-based controller is designed to address complex situations where system states are difficult to measure directly.Secondly,unlike the limited cascade and ring topology connections in previous results,this study considers a universal arbitrary topology.Furthermore,it is noteworthy that the plug-and-play(PnP)capability of LSSs is guaranteed thanks to the proposed scalable scheme.Specifically,when subsystems are added or removed,only the controller gains of directly connected neighbors need updating,eliminating the need to redesign the entire system.Moreover,by choosing a Lyapunov-Krasovskii function with a quadratic matrix-valued polynomial,sufficient conditions are deduced to guarantee the global exponential stability with the desired extended dissipative performance for the resulting LSSs.Finally,the effectiveness of the employed scheme is verified by numerical and microgrid examples.
文摘From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.
文摘By combining all optical,electronic,and mechanical capabilities,electro-optomechanical systems,along with the use of mechanical displacement,the conversion of low-frequency electrical signals into much higher-frequency optical signals is possible.This process provides several capabilities that have very important applications in various fields,including classical,as well as quantum communications.In this regard,the inevitable effect of dissipation on the performance indicators of such systems is one of the important issues affecting its efficiency.One approach for investigating the effect of dissipation is based on a time-dependent Hamiltonian has been known as the Caldirola-Kanai(CK)Hamiltonian,wherein the exponentially increasing mass,i.e.m(t)=m0(eγt)enters the mechanical oscillator system.Utilizing this approach shows that,the performance of the system under the influence of dissipation with CK Hamiltonian formalism,in which the dissipation terms are embedded in the Hamiltonian,are more logical,analytical,and reliable than considering the effect of dissipation with the phenomenological method(including the dissipation effects in the equations of motion by hand),which has been recently used in Bagci et al.(Nature,507,81,2014).In our method,it is also possible to monitor the performance of the system via the adjustment of dissipation components,i.e.,resistance R and reactance L(and CK damping parameterγ)in the electrical(mechanical membrane)part of the system.
文摘More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.
文摘This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These models offer valuable insights into nonlinear wave propagation,with applications in fluid dynamics and materials science,including systems such as liquid crystals and ferrofluids.It is shown that the conservative Sawada-Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles,as well as two-and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation(ODE)system.For the dissipative generalized Sawada-Kotera equation,chaotic wave behavior is observed.The transition to chaos in the corresponding ODE systemfollows a universal bifurcation scenario consistent with the framework established by FShM(Feigenbaum-Sharkovsky-Magnitskii)theory.Notably,this study demonstrates for the first time that the conservative Sawada-Kotera equation can exhibit complex quasi-periodic wave solutions,while its dissipative counterpart admits an infinite number of stable periodic and chaotic waveforms.
基金supported by the Natural Science Foundation of China(11001095)the Ph.D.specialized grant of the Ministry of Education of China(20100144110001)+2 种基金the Special Fund for Basic Scientific Research of Central Colleges(CCNU12C01001)supported by the Fundamental Research Funds for the Central Universities(2015IA009)the Natural Science Foundation of China(61573012)
文摘This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx＋（ζθ）x＋aθxx,ζt=-θx＋βζxx;with initial data and end states （ζθ）（x,0）=（ζ0,θ0）（x）→（ζ±,θ±）as x→∞.We obtain the existence of traveling wave solutions by phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without restrictions on the coeffi- cients a and v by the method of energy estimates.
基金partially supported by NNSF of China(11571126,11701198)China Postdoctoral Science Foundation funded project(2017M622397)
文摘This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.
基金supported by the Major Program of National Natural Science Foundation of China(60710002)the Program for Changjiang Scholars and Innovative Research Team in University.
文摘This article is concerned with the problem of robust dissipative filtering for continuous-time polytopic uncertain neutral systems. The main purpose is to obtain a stable and proper linear filter such that the filtering error system is strictly dissipative. A new criterion for the dissipativity of neutral systems is first provided in terms of linear matrix inequalities （LMI）. Then, an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems. Two numerical examples are given. One illustrates the less conservativeness of the proposed criterion; the other demonstrates the validity of the filtering design procedure.
基金the National NSFC under grant No.50579022the Foundation of Pre-973 Program of China under grant No.2004CCA02500+1 种基金the SRF for the ROCS,SEMthe Talent Recruitment Foundation of HUST
文摘The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.
基金The Natural Science Foundation of Yun-nan Province of China (2001A0001M)
文摘By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.
文摘In this paper we develop a kind of dissipative discrete scheme for the computation of homoclinic orbits near TB-point in Hamiltonian systems. It is proved by using continuation method that when the dissipative term and its coefficient are suitably chosen, this scheme possesses discrete homoclinic orbits, which approximate the continuous homoclinic orbits with second order accuracy w.r. to time-step size.
文摘This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special cases. The paper is concerned with the design of dissipative static state feedback controllers such that the closed-loop system is (robustly) asymptotically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative state feedback controllers are obtained by using a linear matrix inequality (LMI) approach. It is shown that the solvability of dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H ∞ control and passive control.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12064012 and 11374096).
文摘The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory.We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment.Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla.Particularly,via preparing the state of the system to the highest excited state with hight fidelity,the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously.We explain these results using the definition of state fidelity.Furthermore,we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control.Therefore,our results may be of importance in the context of quantum information technologies.
