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

Published

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

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 June 18, 2024)

Issues

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Created September 1, 2002, Updated February 19, 2017