Dynamics and Circuit Implementation of a 4D Memristive Chaotic System with Extreme Multistability

In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values x(0), z(0) and u(0) of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the u-coordinate, which verifies the initial-offset boosting behavior of the system. Then the complex dynamical behavior of the system is studied in detail through the phase portraits of coexisting attractors, the average value of state variables, Lyapunov exponent spectrum, bifurcation diagram, attraction basin and the complexity of spectral entropy (SE). In addition, the simulation of the Multisim circuit is also carried out, and the results of numerical simulation and analog circuit simulation are consistent. Finally, the chaotic sequence generated by the system is applied to image encryption, and according to the performance analysis, the proposed chaotic system has good security performance.

Automated summary

In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with a cosine function is constructed. It has infinitely many equilibria. The distribution of infinitely many single-wing and double-wing attractors along the u-coordinate is obtained by changing the initial values of the system and keeping the parameters constant, verifying the initial-offset boosting behavior of the system. Additionally, the complex dynamical behavior of the system is studied in detail through various analysis techniques, and the proposed chaotic system is applied to image encryption and shows good security performance.