We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m...We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.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
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin...Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.展开更多
This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perf...This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.展开更多
Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the v...Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.展开更多
We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The conver...We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems （mainly the Lorenz and Chen systems）. The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.展开更多
The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy h...The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.展开更多
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a...Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.展开更多
Distributed state estimation is of paramount importance in many applications involving the large-scale complex systems over spatially deployed networked sensors.This paper provides an overview for analysis of distribu...Distributed state estimation is of paramount importance in many applications involving the large-scale complex systems over spatially deployed networked sensors.This paper provides an overview for analysis of distributed state estimation algorithms for linear time invariant systems.A number of previous works are reviewed and a clear classification of the main approaches in this field are presented,i.e.,Kalman-filter-type methods and Luenberger-observer-type methods.The design and the stability analysis of these methods are discussed.Moreover,a comprehensive comparison of the existing results is provided in terms of some standard metrics including the graph connectivity,system observability,optimality,time scale and so on.Finally,several important and challenging future research directions are discussed.展开更多
A control method is presented for the problem of decentralized stabilizationof large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. An uncertainty toleranc...A control method is presented for the problem of decentralized stabilizationof large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. An uncertainty tolerance matrix is defined to characterize thedesired robustness leve1 of the overall system. It is then identified that, for a given uncer-tainty tolerance matrix, the design problem is related to the existence of a smooth Positivedefinite solution to a modified Ham ilton -Jacobi - Bellman (H-J-B ) equa tion. The solution,if exists, is exactly the payoff function in terms of the game theory. A decentralized statefeedback law is duly designed, which, under the weak assumption of the zero-state ob-servability on the system, renders the overall closed-loop system aspoptotically stable withan explicitly expressed stability region. Finally, relation between the payoff function andthe uncertainty tolerance matrix is provided, highlighting the 'knowing less and payingmore' philosophy.展开更多
This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient c...This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented.展开更多
We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order deriv...We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.展开更多
We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration do...We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).展开更多
In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.
In this paper, we present an innovative non–linear, discrete, dynamical system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that h...In this paper, we present an innovative non–linear, discrete, dynamical system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that have passed since this famous naval battle which took place in late September 480 B.C. The suggested model describes very well the most effective strategic behavior between two participants during a battle (or in a war). Moreover, we compare the results of the Dynamical Systems analysis to Game Theory, considering this conflict as a “war game”.展开更多
The use of functions, expressible in terms of Lucas polynomials of the second kind, allows us to write down the solution of linear dynamical systems—both in the discrete and continuous case—avoiding the Jordan...The use of functions, expressible in terms of Lucas polynomials of the second kind, allows us to write down the solution of linear dynamical systems—both in the discrete and continuous case—avoiding the Jordan canonical form of involved matrices. This improves the computational complexity of the algorithms used in literature.展开更多
Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems und...Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems under consideration admit monotonic nondecreasing traveling waves.展开更多
Using information theory,this study provides insights into how the construction of latent space of autoencoder(AE)using deep neural network(DNN)training finds a smooth(non-stiff)low-dimensional manifold in the stiff d...Using information theory,this study provides insights into how the construction of latent space of autoencoder(AE)using deep neural network(DNN)training finds a smooth(non-stiff)low-dimensional manifold in the stiff dynamical system.Our recent study(Vijayarangan et al.2023)reported that an AE combined with neural ODE(NODE)as a surrogate reduced order model(ROM)for the integration of stiff chemically reacting systems led to a significant reduction in the temporal stiffness,and the behavior was attributed to the identification of a slow invariant manifold by the nonlinear projection using the AE.The present work offers a fundamental understanding of the mechanism of formation of a non-stiff latent space and stiffness reduction by employing concepts from information theory and better mixing.The learning mechanisms of both the encoder and the decoder are explained by plotting the evolution of mutual information and identifying two different phases.Subsequently,the density distribution is plotted for the physical and latent variables,which shows the transformation of the rare event in the physical space to a highly likely(more probable)event in the latent space provided by the nonlinear autoencoder.Finally,the nonlinear transformation leading to density redistribution is explained using concepts from information theory and probability.展开更多
The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in componen...The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in learning.To overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system learning.The MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale module.The Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning problem.The multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in velocity.Experimental results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions.展开更多
For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The propose...For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.展开更多
基金Project supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20220917)the National Natural Science Foundation of China (Grant Nos.12001213 and 12302035)。
文摘We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
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.
文摘Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.
基金The project supported by National Natural Science Foundation of China under Grant No.60674040National Natural Science Foundation for Distinguished Young Scholars under Grant No.60225015
文摘This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
基金the National Natural Science Foundation of China (11871188, 12031019)。
文摘Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.
基金Supported by the National Natural Science Foun-dation of China (60133010) the Natural Science Foundation ofHubei Province (2004ABA011)
文摘We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems （mainly the Lorenz and Chen systems）. The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.
文摘The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.
文摘Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.
基金supported by the National Natural Science Foundation of China (No. 61790573)supported by the National Natural Science Foundation of China (Nos. 61890924, 61991404)Liao Ning Revitalization Talents Program (No. XLYC1907087)
文摘Distributed state estimation is of paramount importance in many applications involving the large-scale complex systems over spatially deployed networked sensors.This paper provides an overview for analysis of distributed state estimation algorithms for linear time invariant systems.A number of previous works are reviewed and a clear classification of the main approaches in this field are presented,i.e.,Kalman-filter-type methods and Luenberger-observer-type methods.The design and the stability analysis of these methods are discussed.Moreover,a comprehensive comparison of the existing results is provided in terms of some standard metrics including the graph connectivity,system observability,optimality,time scale and so on.Finally,several important and challenging future research directions are discussed.
文摘A control method is presented for the problem of decentralized stabilizationof large scale nonlinear systems by designing robust controllers, in the sense of L2-gaincontrol, for each subsystem. An uncertainty tolerance matrix is defined to characterize thedesired robustness leve1 of the overall system. It is then identified that, for a given uncer-tainty tolerance matrix, the design problem is related to the existence of a smooth Positivedefinite solution to a modified Ham ilton -Jacobi - Bellman (H-J-B ) equa tion. The solution,if exists, is exactly the payoff function in terms of the game theory. A decentralized statefeedback law is duly designed, which, under the weak assumption of the zero-state ob-servability on the system, renders the overall closed-loop system aspoptotically stable withan explicitly expressed stability region. Finally, relation between the payoff function andthe uncertainty tolerance matrix is provided, highlighting the 'knowing less and payingmore' philosophy.
文摘This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented.
文摘We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.
文摘We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).
文摘In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.
文摘In this paper, we present an innovative non–linear, discrete, dynamical system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that have passed since this famous naval battle which took place in late September 480 B.C. The suggested model describes very well the most effective strategic behavior between two participants during a battle (or in a war). Moreover, we compare the results of the Dynamical Systems analysis to Game Theory, considering this conflict as a “war game”.
文摘The use of functions, expressible in terms of Lucas polynomials of the second kind, allows us to write down the solution of linear dynamical systems—both in the discrete and continuous case—avoiding the Jordan canonical form of involved matrices. This improves the computational complexity of the algorithms used in literature.
文摘Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c<sub>*</sub>>0 such that for each c≥c*</sub>, the systems under consideration admit monotonic nondecreasing traveling waves.
基金funded by King Abdullah University of Science and Technology(KAUST)。
文摘Using information theory,this study provides insights into how the construction of latent space of autoencoder(AE)using deep neural network(DNN)training finds a smooth(non-stiff)low-dimensional manifold in the stiff dynamical system.Our recent study(Vijayarangan et al.2023)reported that an AE combined with neural ODE(NODE)as a surrogate reduced order model(ROM)for the integration of stiff chemically reacting systems led to a significant reduction in the temporal stiffness,and the behavior was attributed to the identification of a slow invariant manifold by the nonlinear projection using the AE.The present work offers a fundamental understanding of the mechanism of formation of a non-stiff latent space and stiffness reduction by employing concepts from information theory and better mixing.The learning mechanisms of both the encoder and the decoder are explained by plotting the evolution of mutual information and identifying two different phases.Subsequently,the density distribution is plotted for the physical and latent variables,which shows the transformation of the rare event in the physical space to a highly likely(more probable)event in the latent space provided by the nonlinear autoencoder.Finally,the nonlinear transformation leading to density redistribution is explained using concepts from information theory and probability.
基金supported by the National Natural Science Foundations of China(Nos.12172186 and 11772166).
文摘The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in learning.To overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system learning.The MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale module.The Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning problem.The multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in velocity.Experimental results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions.
基金Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(Grant No.GZC20231050)the National Natural Science Foundation of China(Grant Nos.12175193 and 11905183)the 13th Five-year plan for Education Science Funding of Guangdong Province(Grant No.2021GXJK349)。
文摘For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.
