A Memristor - Based Hyperchaotic System with Hidden Attractors : Dynamics , Synchronization and Circuital Emulating

Abstract

Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention recently. A memristor-based hyperchaotic system with hidden attractor is studied in this paper. The dynamics properties of this hyperchaotic system are discovered through equilibria, Lyapunov exponents, bifurcation diagram, Poincaré map and limit cycles. In addition, its anti-synchronization scheme via adaptive control method is also designed and MATLAB simulations are shown. Finally, an electronic circuit emulating the memristor-based hyperchaotic system has been designed using off-the-shelf components.

Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

“…Subsequent studies of this work will consider more aspects for chaos based secure communication, utilizing systems with hidden attractors. These include systems of higher dimension, hyperchaotic systems [15,22], and discrete time systems [69,70]. Also, the transmission of different types of signals, for example for image transmission will also be considered, and also the nonlinear transmission of the information signal.…”

“…Over the years, chaos synchronization has found applications in many scientific disciplines, including, but not limited to, encryption and secure transmission [2][3][4][5][6][7][8], optics and lasers [9,10], engineering [11] and robotics [12][13][14]. So far, a wide variety of design approaches have been applied for synchronization [2,[15][16][17][18][19][20][21][22][23][24].…”

Synchronization of Periodic Self-Oscillators Interacting via Memristor-Based Coupling

“…There are examples of memristorbased chaotic oscillators [10][11][12][13] and Hamiltonian systems including the memristor [14]. A variety of the effects in memristor oscillators is complemented by the existence of hidden attractors [15][16][17] and manifolds of equilibria (in the simplest case it is a line of equilibria) in the phase space [18][19][20][21][22][23][24][25][26].…”

Adaptive Control Synchronization of a Novel Memristive Chaotic System for Secure Communication Applications

“…Moreover, Buscarino et al [16] introduced a new chaotic oscillator-based HP memristor model; they produced new chaotic signals by using the HP memristor model. Pham et al [17] suggested an adaptive synchronization scheme for a memristor hyper-chaotic system in which an adaptive control method is used for designing an anti-synchronization scheme for the memristor system. The Arduino microcontroller has also been used to implement and develop the chaotic memristor system as in [18].…”