Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Method in Engineering, Physics, and Neuroscience

Published

September 1, 2002

Author(s)

Emil Simiu

Abstract

The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This paper describes and illustrates a unified treatment of deterministic and stochastic systems that extends the applicability of the classical Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, colored, or dichotomous noise. The extended method yields the novel result that motions with transitions are chaotic for either deterministic or stochastic excitation, explains the role in the occurrence of transitions of the system and excitiation characteristics, and is a powerful modeling and identification tool.

Proceedings Title

Structural Dynamics EURODYN2002 | 5th | | Balkema

Volume

1

Conference Dates

September 2-5, 2002

Conference Location

Munich, GE

Conference Title

European Conference on Structural Dynamics

Pub Type

Conferences

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Keywords

building technology, chaos, Melnikov processes, system identification

Citation

Simiu, E. (2002), Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Method in Engineering, Physics, and Neuroscience, Structural Dynamics EURODYN2002 | 5th | | Balkema, Munich, GE, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=860390 (Accessed December 13, 2024)