Chaotic Transitions in Deteffi1inistic and Stochastic Dynamical Systems: Applications of the Melnikov Method in Engineering, Physics,

ABSTRACT: The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit trarlsitions, i.e. escapes from and captures into preferred regions of phase space. This paper describes and illustratt:s a unified treatment of deterministic and stochastic systems that extends the ap-plicability 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 £Dr either deterministic or stochastic excitation, explains the role in the occurrence of transitions of the system and excitation characteristics, and is a powerful modeling and identification tool