Continuation-Based Method to Find Periodic Windows in Bifurcation Diagrams With Applications to the Chua’s Circuit With a Cubic Nonlinearity

Abstract

The existence of periodic windows in the parameter space is a common feature of nonlinear systems capable to produce chaotic behavior. Detection of positions of periodic windows is important both from the theoretical and practical points of view. In this work, a systematic method to detect periodic windows in bifurcation diagrams is proposed. The search method is a combination of the trajectory monitoring approach to find unstable periodic orbits and the continuation method to calculate positions of periodic windows. The method is applied to the Chua's circuit with a smooth nonlinearity. It is shown that the proposed method outperforms standard methods to find periodic windows in bifurcation diagrams.