A novel dual memristor hyperchaotic system and its application for secure communication based on three‐fold function projection synchronization

Abstract

AbstractA novel simplest four‐dimensional hyperchaotic system with dual memristors is designed by using a charge‐controlled memristor and a generalized voltage‐controlled memristor. Based on the conventional dynamic analysis method and MATLAB simulation software, the dynamic characteristics of the dual memristor hyperchaotic system such as Lyapunov exponent spectrum, phase diagram, and bifurcation diagram are studied. The novel system is found to exhibit singular nonlinear phenomena, such as limit cycle, state transition and multiple scroll attractor with certain parameter values. Being different from most known chaotic systems, which contain only two isolated unstable equilibrium points, the novel system has an infinite number of unstable equilibriums points and a larger Lyapunov exponent. What is more, the three‐fold function projection synchronization of the dual memristor hyperchaotic system and its application for secure communication is studied. Based on Lyapunov stabilization theory and adaptive sliding mode control method, three driving systems and three response systems are synchronized according to the corresponding scaling function matrix, respectively. In the secure communication system, the message signal is separated into three parts loaded in the different drive systems with different initial conditions to increase the reliability. The corresponding numerical simulations demonstrate the effectiveness of the results obtained.