Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

Abstract

In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.