Bifurcation of Oscillation Modes Obtained by a Shift Type Mapping Simulating the Oregonator Responding to an External Periodic Force

Abstract

We have simulated the Oregonator by “shift type mapping” functions which approximate the strange attractor of the Oregonator (a system governed by a set of non-linear differential equations) exerted by an external periodic force. We have reproduced fairly well the bifurcation and the sequential appearance of the periodic π(m) modes and π_p,q(m, m+1) modes as well as chaotic modes. The theoretical prediction of the oscillation modes using a piecewise linear mapping function agrees qualitatively with the results of the Oregonator and those using other mapping functions.