Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Processes in Engineering, Physics, and Neuroscience.
Chaotic Transitions in Deterministic and Stochastic
Dynamical Systems: Application of Melnikov Processes in
Engineering, Physics, and Neuroscience.
Structural Dynamics, 5th European Conference.
EURODYN2002. Proceedings. Septemer 2-5, 2002, Munich,
Germany, 179-183 pp, 2002.
deterministic planar systems; chaos; Melnikov processes;
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