Controlling Bifurcation in Electronic Implementation of Dynamical Systems

Abstract

In the theoretical and experimental studies of bifurcations in dynamical systems, the adjustments of the parameter values play a key role. The reason is because small variations in these values may result in topological changes in the behavior of the flow of the system. Taking this into account, in this paper, a new design for controlling bifurcation, suitable for electronic implementations of chaotic systems, is presented. The variation of the bifurcation parameter is performed by means of an Arduino UNO micro-controller and a digital controlled potentiometer. In this way, the variation of the electronic components is performed in an automated manner, avoiding the intrinsic problems of a manual variation of the circuit parameters. As a particular example, a scaled Rössler system is considered. One of the advantages of the controlled automated bifurcation is that it is useful for analyzing the robustness of the different limiting behaviors of the system against parameter mismatches.