Nonlinear Dynamics in the Coupled Fractional-Order Memristor Chaotic System and Its Application in Image Encryption

Abstract

This work presents two forms of coupled fractional-order memristor chaotic systems. The existence and uniqueness of solutions are studied. Moreover, the range of parameters and time span at which the proposed two models exhibit continuous dependence on initial conditions are examined. The unique equilibrium point for each system is found, and the corresponding stability analysis is carried out. The regions of stability in the space of parameters are obtained, whereas numerical simulations are employed to confirm theoretical results. The bifurcation diagrams, in addition to Lyapunov exponents, are utilized to examine the effects of key parameters in two models. A chaos-based encryption scheme is presented as an application to utilize complicated chaotic behaviors in coupled circuits.