A hyperchaotic memristive system with extreme multistability and conservativeness

Comparing with dissipative systems, conservative systems have distinguished advantages in information processing and secure communication. It is of practical importance and theoretical significance to design conservative chaotic systems based on memristors due to their special features of complexity and flexibility. In this paper, a novel conservative hyperchaotic memristor system is proposed. The rich dynamics of the system, including extreme multistability and hyperchaos, are analyzed by using phase portraits, time series, bifurcation diagrams and Lyapunov exponents, and confirming the system is conservative. Based on the Hamiltonian theory, a specific energy function of the system is constructed and the generation mechanism of the extreme multistability is revealed and analyzed. Interestingly, a special heart-shaped attractor is found from the system. Finally, the theoretical results are verified and demonstrated through physical circuit implementation, demonstrating its potential for future applications.