Analysis of a novel fractional-order chaotic circuit with a feedback memristor: design, dynamics, and application

Abstract

In this research, a novel fractional-order chaotic circuit incorporating a feedback memristor is presented. The structure of the circuit and the associated mathematical model are described in detail. The complex dynamics of the circuit are analyzed using stability analysis, Poincaré maps and numerical simulations, revealing the presence of a saddle fixed point and coexisting attractors. The influence of changing the system variables and initial conditions is studied using bifurcation plots and Lyapunov exponents. The circuit exhibits a variety of nonlinear behaviours including periodic, quasi-periodic, and chaotic dynamics. Furthermore, experimental simulations performed with a chain-ship circuit configuration validate the theoretical results and show strong agreement with the numerical analysis. Finally, a robust sound encryption scheme is presented that exploits the pseudorandom sequences generated by the chaotic memristive circuit.