- Author
- Simiu, E. | Frey, M. R. | Hagwood, C.
- Title
- Melnikov Necessary Condition for Noise-Induced Escapes.
- Coporate
- National Institute of Standards and Technology, Gaithersburg, MD Bucknell Univ., Lewisburg, PA
- Sponsor
- Office of Naval Research, Washington, DC
- Contract
- ONR-GRANT-N00014-94-0028 ONR-GRANT-N00014-94-0284
- Book or Conf
- International Association for Civil Engineering Reliability and Risk Analysis (CERRA). International Conference on ICASP, 7th Proceedings. Applications of Statistics and Probability. Civil Engineering Reliability and Risk Analysis. July 10-13, 1995, A.A. Balkema, Rotterdam, Paris, France, Lemaire, M.; Favre, J. L.; Mebarki, A., Editors, 1137-1142 p., 1995
- Keywords
- noise (sound) | Melnikov function | equations | escape means
- Identifiers
- dynamical systems; Melnikov functions and processes; upper bound for mean exit rate; systems with noise having tail-limited marginal distrubution
- Abstract
- For a wide class of nonlinear multistable deterministic systems, a necessary condition for the occurrence of chaos - and jumps between phase space regions associated with potential wells - is that the system's Melnikov function have simple zeros. The work presented in this paper is based on our extension of the Melnikov-based approach to a class of nonlinear stochastic differential equations with additive or multiplicative noise. The mean zero upcrossing rate for the stochastic system's Melnikov process is a weak upper bound for the system's mean escape rate. For systems excited by processes with tail-limited distributions the stochastic Melnikov approach yields a simple criterion guaranteeing the non-occurrence of chaos. This is illustrated for excitation by square wave, coin-toss dichotomous noise.