- Author
- Simiu, E.
- Title
- Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Processes in Engineering, Physics, and Neuroscience.
- Coporate
- National Institute of Standards and Technology, Gaithersburg, MD
- Book or Conf
- Structural Dynamics, 5th European Conference. EURODYN2002. Proceedings. Septemer 2-5, 2002, Munich, Germany, 179-183 p., 2002
- Keywords
- deterministic planar systems | chaos | Melnikov processes | system identification
- Identifiers
- Melnikov functions and processes; necessary condition for the occurrence of exits; vessel capsizing; open-loop control of escapes; stochastic resonance; snap-through of a transversely excited buckled column; wind-induced along-shore currents over ocean floor with variable topography; auditory nerve system as a chaotic dynamical system
- 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.