Modified projective synchronization of fractional-order hyperchaotic memristor-based Chua’s circuit

Abstract

This paper investigates the modified projective synchronization (MPS) between two hyperchaotic memristor-based Chua circuits modeled by two nonlinear integer-order and fractional-order systems. First, a hyperchaotic memristor-based Chua circuit is suggested, and its dynamics are explored using different tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams. Another interesting property of this circuit was the coexistence of attractors and the appearance of mixed-mode oscillations. It has been shown that one can achieve MPS with integer-order and incommensurate fractional-order memristor-based Chua circuits. Finally, examples of numerical simulation are presented, showing that the theoretical results are in good agreement with the numerical ones.

A secure communication scheme based on generalized modified projective synchronization of a new 4-D fractional-order hyperchaotic system

“…Some methods and techniques have been introduced to control and synchronize fractional-order chaotic systems based on this consideration, such as adaptive control [36], active control [37], sliding mode control [38], and so on. Adopting the previous methods, different types of chaotic and hyperchaotic synchronizations have appeared, such as complete synchronization [39], generalized synchronization [40], anti-synchronization [41], phase synchronization [42], modified projective synchronization [43], etc…”