Study of Evolution of Global Structure Into Chaotic Itinerancy by Point Mapping Under Cell Reference Method

Abstract

Chaotic itinerancy is a complex phenomenon in high-dimensional dynamic systems, by which an orbit successively itinerates over low-dimensional semi-stable invariant sets in a chaotic manner. In this paper the evolution of the global structure of the coupled neural oscillators into the chaotic itinerancy is investigated by using an extended Point Mapping under Cell Reference Method. The method of Point Mapping under Cell Reference, denoted as PMUCR in short, was a numerical method developed for the global analysis of nonlinear dynamical systems with the aim to retain the accuracy of Point Mapping Method but enhance its computational efficiency. The method is extended to be able compute both stable and unstable invariant sets in highdimensional dynamical systems by taking the virtue of the cell structure and incorporate with PIM-triple method. By applying extended PMUCR method to the coupled Morris-Lecar neuron model, some important global structure changes in invariant sets during the evolution into the chaotic itinerancy are demonstrated.