A Novel Two-Memristor Hyperchaotic System with Rich Dynamics and its Synchronization Application

Abstract

A novel two-memristor hyperchaotic system is obtained by adding a cubic magneto-controlled memristor to a memristor chaotic system. The dynamics are analyzed by Lyapunov exponents, complexity, 0-1 test, bifurcation diagram and phase diagram. In addition, the new system has complex dynamic behaviors of transient chaos, transient transition, intermittent chaos and offset-boosting. Remarkably, for fixed parameters, a rare phenomenon of coexisting chaotic, periodic, and stable unfixed point attractors could be found in the new system. Moreover, through circuit design, the simulation based on Multisim confirms the consistency between numerical calculations, thereby verifying the accuracy of memristive chaotic system. Finally, the coupling synchronization and tracking synchronization methods are designed, which has significant implications for theoretical research and engineering applications.

Keywords: memristor, coexisting attractors, intermittent chaos, offset-boosting, Synchronization