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

Abstract

This paper introduces a new memristor-based hyperchaotic complex Lü system (MHCLS) and investigates its adaptive complex generalized synchronization (ACGS). Firstly, the complex system is constructed based on a memristor-based hyperchaotic real Lü 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.

Heterogeneous Memristive Models Design and Its Application in Information Security

“…In 2008, Strukov and his colleagues of Hewlett-Packard (HP) Labs fabricated a nanometer-sized TiO2 memristor, the features of the circuit are consistent with the characteristics of the resistive device predicted by Leon O. Chua [Strukov, Snider, Stewart et al (2008)]. In 2010, HP Labs once again announced that the memristor apparatus has Boolean logic operation function, this discovery shocked the computer field [Vaidyanathan, Pham and Volos (2017); Duan, Zhang and Hu et al (2014); Qu, Zhu and Wang et al (2018) Hence, the research of memristor has been widely developed and applied in various fields [Peishin and Di Ventra (2011); Yakopcic, Hasan and Taha (2017); Wang, Wang and Zhou (2016)]. Researchers in Germany have produced learning-capable nanomemristor devices, each of them is only 600 times the diameter of a human hair [Thomas (2013)].…”

Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization

“…A Murali-Lakshmanan-Chua's circuit with a piecewise linear active flux controlled memristors with hyperchaotic behavior was investigated by Ishaq Ahamed and Lakshmanan [15]. A memristor based hyperchaotic complex Lu system and its adaptive synchronization were studied by Wang et al [16].…”

A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

“…Complex modified generalized projective synchronization (CMGPS) [18] and complex modified hybrid projective synchronization (CMHPS) [19] were executed between the same or different dimensional partial request complex chaotic (hyperchaotic). Complex generalized synchronization as for a mind-boggling vector map [20,21] was presented for two indistinguishable or nonidentical chaotic (hyperchaotic) complex-variable systems. The complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters was studied in [22,23] while the complex modified function projective synchronization of complex chaotic systems is investigated in [24,25].…”

“…Complex synchronization of chaotic (hyperchaotic) complex systems is a critical nonlinear occurrence [13][14][15][16][17][18][19][20][21][22][23][24][25]. Complex synchronization of chaotic complex systems considers a couple of complex chaotic systems called main and slave systems, and it means to accomplish asymptotic tracking of the conditions of the slave system to the conditions of the main system.…”