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
Nonlinear and stochastic dynamics is essential and practical in almost all branches of natural science and engineering.It has been a central subject to understand various complex dynamics,such as random vibration,stoc...Nonlinear and stochastic dynamics is essential and practical in almost all branches of natural science and engineering.It has been a central subject to understand various complex dynamics,such as random vibration,stochastic transition,synchronization,et al.,in the areas of mechanical and aerospace engineering,physics and chemistry.For example,the stochastic resonance has been utilized effectively in mechanical fault diagnosis and weak signal detection.Naturally,many methods have been developed to get the stochastic responses,including stochastic averaging method.展开更多
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Nonlinear and stochastic dynamics is essential and practical in almost all branches of natural science and engineering.It has been a central subject to understand various complex dynamics,such as random vibration,stochastic transition,synchronization,et al.,in the areas of mechanical and aerospace engineering,physics and chemistry.For example,the stochastic resonance has been utilized effectively in mechanical fault diagnosis and weak signal detection.Naturally,many methods have been developed to get the stochastic responses,including stochastic averaging method.
