Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently...Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.展开更多
The modeling and dynamical analysis of discrete chaotic systems is a vital research field,and various chaotic maps have been developed using mathematical and control-theoretic approaches.However,physical circuit desig...The modeling and dynamical analysis of discrete chaotic systems is a vital research field,and various chaotic maps have been developed using mathematical and control-theoretic approaches.However,physical circuit design of mathematically defined discrete chaotic systems and the computation of their energy functions remain challenging and open problems.In this study,a two-dimensional(2D)chaotic map is constructed using an open-loop modulation coupling method,and its dynamical characteristics are analyzed using bifurcation diagrams.Lyapunov exponents(LEs)and spectral entropy(SE)complexity are also inspected under different parameter configurations.Furthermore,the proposed chaotic map is expressed using two distinct physical memristive circuits:one is composed of a magnetic flux-controlled memristor,a nonlinear resistor,and a capacitor;the other utilizes a charge-controlled memristor,a nonlinear resistor,and an inductor.Moreover,two energy functions are derived from the two memristor-coupled circuits for the proposed chaotic map.The results demonstrate that the mathematical model of the discrete chaotic system can be effectively expressed through these two nonlinear circuits.Our study offers a theoretical foundation and viable methodology for the physical circuit representation of discrete chaotic systems and determination of their energy functions.展开更多
基金Project supported by the National Natural Science Foundation of China(No.12402033)the National Natural Science Foundation for Distinguished Young Scholars of China(No.52225211)。
文摘Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.
基金supported by the National Natural Science Foundation of China(No.62301416).
文摘The modeling and dynamical analysis of discrete chaotic systems is a vital research field,and various chaotic maps have been developed using mathematical and control-theoretic approaches.However,physical circuit design of mathematically defined discrete chaotic systems and the computation of their energy functions remain challenging and open problems.In this study,a two-dimensional(2D)chaotic map is constructed using an open-loop modulation coupling method,and its dynamical characteristics are analyzed using bifurcation diagrams.Lyapunov exponents(LEs)and spectral entropy(SE)complexity are also inspected under different parameter configurations.Furthermore,the proposed chaotic map is expressed using two distinct physical memristive circuits:one is composed of a magnetic flux-controlled memristor,a nonlinear resistor,and a capacitor;the other utilizes a charge-controlled memristor,a nonlinear resistor,and an inductor.Moreover,two energy functions are derived from the two memristor-coupled circuits for the proposed chaotic map.The results demonstrate that the mathematical model of the discrete chaotic system can be effectively expressed through these two nonlinear circuits.Our study offers a theoretical foundation and viable methodology for the physical circuit representation of discrete chaotic systems and determination of their energy functions.
