Complex Dynamics of the Chua’s Circuit System with Adjustable Symmetry and Nonlinearity: Multistability and Simple Circuit Realization

Abstract

Background: Since the invention of Chua’s circuit, numerous generalizations based on substitution of the nonlinear function have been reported. One of the generalizations is obtained by replacing the piecewise-linear with the cubic and/or quadratic polynomial. These nonlinearities are used to be implement using analog multipliers which are relatively expensive. In this realization we propose a different approach to synthetize both cubic and quadratic nonlinearities of empirical Chua’s circuit. Methods: The idea is to use diodes, Opamps and resistors to derive a PWL approximation of the cubic and quadratic functions. To demonstrate some complex phenomena observed in the system using the fourth order Runge-Kutta numerical integration method with a very small integration step. The bifurcation diagram which is the plot of local maxima of the temporal trace of a system’s coordinate as a function of the control parameter also constitutes an excellent tool for the study of dynamic systems. Results: The above mentioned standard nonlinear analysis tools have been exploited and it is found that the system with adjustable symmetry experiences a plethora of symmetric and asymmetric coexisting attractors. A particular feature of the system is related to the simplicity of the corresponding electronic analog circuit (no analog multiplier chip used to implement the cubic and quadratic nonlinearities). Conclusions: It is observed that the proposed Chua’s circuit system is more flexible (both symmetric and asymmetric) and displays complex dynamics behaviors of symmetric and asymmetric coexisting attractors. Note that this striking dynamic can be exploited in encryption algorithms.