Poincare Linear Interpolated Cell Mapping: Method for Global Analysis of Oscillating Systems

Abstract

A method for global analysis of nonlinear dynamical oscillating systems was developed. The method is based on the idea of introducing a Poincare section into a multidimensional state space of the dynamical system and combine it with an interpolation procedure within the cells which constitute the discretized problem domain of interest. The proposed method was applied to study the global behavior of two nonlinear coupled van der Pol oscillators. Significant saving in calculation time, in comparison with both direct numerical integration and Poincare-like simple cell mapping, is demonstrated.