Synchronization between two chaotic memristor circuits via the flux-charge analysis method

Abstract

Recent articles introduced a new method, named flux-charge analysis method (FCAM), for studying nonlinear dynamics and bifurcations of a large class of memristor circuits. FCAM is based on Kirchhoff flux and charge Laws, and constitutive relations of basic circuits elements, expressed in the flux-charge domain. As such, FCAM is in contrast with other traditional methods for studying the dynamics of memristor circuits, that are instead based on the analysis in the standard voltage-current domain. So far, FCAM has been used to study saddle-node bifurcations of equilibrium points in the simplest memristor circuit composed of an ideal flux-controlled memristor and a capacitor, and more complex Hopf and period doubling bifurcations in certain classes of second- and third-order oscillatory memristor circuits. These bifurcations may be induced by varying initial conditions for a fixed set of circuit parameters (bifurcations without parameters). A peculiar property proved via FCAM is that the state space of a memristor circuit can be decomposed in infinitely many invariant manifolds, where each manifold is characterized by a different reduced-order dynamics and attractors. In this paper, FCAM is used for studying synchronization phenomena that can be observed in resistively-coupled arrays of chaotic memristor circuits. In particular, the paper considers two coupled memristor circuits such that each uncoupled circuit displays a double-scroll chaotic attractor on a certain invariant manifold. It is demonstrated via simulations how phase-synchronization of the two coupled attractors can be achieved depending on the choice of the coupling strength.