Hidden Dynamics of Coexisting Periodic Motions for a Piecewise Nonlinear System with Memristive Chua’s Circuit

Chua’s circuit is designed to physically generate chaos, with chaotic behavior existing over a wide range of the system parameters. However, capturing the unstable routes of periodic motions in such a circuit system remains challenging through direct numerical methods, and the bifurcations from periodic motions to chaos often exhibit unusual characteristics. In this paper, the memristive double-scroll Chua’s circuit is studied, which is a recently designed piecewise nonlinear system. A semi-analytical method is proposed to obtain the complete bifurcation diagrams, including many unstable hidden routes. Unusual bifurcations are analyzed via eigenvalue analysis of the Jacobian matrices derived from discretized periodic motions. Furthermore, coexisting periodic motions with similar phase structures are thoroughly examined, revealing distinct dynamic behaviors. The parameter maps are also obtained to show the complex codimension-two bifurcations for such a memristive Chua’s circuit.