A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization

This paper introduces a new memristor-based hyperchaotic complex Lu system (MHCLS) and investigates its adaptive complex generalized synchronization (ACGS). Firstly, the complex system is constructed based on a memristor-based hyperchaotic real Lu system, and its properties are analyzed theoretically. Secondly, its dynamical behaviors, including hyperchaos, chaos, transient phenomena, as well as periodic behaviors, are explored numerically by means of bifurcation diagrams, Lyapunov exponents, phase portraits, and time history diagrams. Thirdly, an adaptive controller and a parameter estimator are proposed to realize complex generalized synchronization and parameter identification of two identical MHCLSs with unknown parameters based on Lyapunov stability theory. Finally, the numerical simulation results of ACGS and its applications to secure communication are presented to verify the feasibility and effectiveness of the proposed method.