Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Processes 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, 5th European Conference. EURODYN2002. Proceedings
Conference Dates
September 2-5, 2002
Conference Location
Munich,

Keywords

deterministic planar systems, chaos, Melnikov processes, system identification

Citation

Simiu, E. (2002), Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Processes in Engineering, Physics, and Neuroscience., Structural Dynamics, 5th European Conference. EURODYN2002. Proceedings, Munich, , [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=916888 (Accessed March 4, 2024)
Created September 2, 2002, Updated February 17, 2017