Chapter 9 - Memristor-based novel 4D chaotic system without equilibria: Analysis and projective synchronization

Abstract

This chapter puts forward the analysis of a novel memristor-based four dimensional (4D) chaotic system without equilibria and its projective synchronization using nonlinear active control technique. The proposed memristor-based novel 4D chaotic system has total nine terms with two nonlinear terms. Different qualitative and quantitative tools: time series, phase plane, Lyapunov exponents, bifurcation diagram, Lyapunov dimension, Poincaré map are used to analyze the proposed memristor-based system. The proposed system has periodic, 2-torus quasi-periodic, chaotic, and chaotic 2-torus attractors, which are confirmed with the calculation of the system's Lyapunov exponents and bifurcation diagram. The proposed chaotic system has thumb and parachute shapes of Poincaré map and satisfy unique and interesting behaviors. Such a memristor-based dissipative chaotic system is not available in the literature. Furthermore, the projective synchronization between memristor-based novel chaotic systems is achieved. The nonlinear active control laws are designed by using the sum of relevant variables of the systems and required global asymptotic stability condition is derived to achieve synchronization. Results are simulated in MATLAB environment and reflect that objectives are achieved successfully.