Synchronization of periodic self-oscillators interacting via memristor-based coupling

TL;DR

This paper investigates how memristor-based coupling affects the synchronization of self-oscillators, revealing the role of nonlinearity and initial conditions in phase locking, and how modifications can eliminate initial condition dependence.

Contribution

It introduces a memristor model for oscillator coupling, analyzes the effects of nonlinearity on equilibrium points, and shows how adding a term can control synchronization behavior.

Findings

Memristor nonlinearity creates a line of equilibria affecting synchronization.

Initial conditions influence the boundaries of the synchronization area.

Adding a small term to the memristor model removes the line of equilibria and initial condition dependence.

Abstract

A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of quasi-harmonic reduction. It is shown that specifics of the memristor nonlinearity results in appearance of infinitely many equilibrium points, which form a line of equilibria in the phase space of the system under study. It is established that possibility to observe the effect of phase locking in the considered system depends both on parameter values and initial conditions. Consequently, boundaries of a synchronization area are determined by the initial conditions. It is demonstrated that addition of a small term into the memristor state equation gives rise to disappearance of the line of equilibria and eliminates the dependence of synchronization on the initial conditions.