Andronov-Hopf bifurcation with and without parameter in a cubic memristor oscillator with a line of equilibria

TL;DR

This paper investigates the bifurcation behavior of a memristor oscillator with a line of equilibria, revealing how oscillations can be triggered by parameter changes or initial conditions, characterized by a unique bifurcation type.

Contribution

It introduces the concept of Andronov-Hopf bifurcation with and without parameter in a memristor oscillator with a line of equilibria, combining numerical and bifurcational analysis.

Findings

Oscillations can be excited via parameter variation or initial conditions.

The bifurcation exhibits features of supercritical Andronov-Hopf bifurcation.

The system has a line of equilibria affecting its bifurcation behavior.

Abstract

The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined with bifurcational analysis. It is shown that oscillation excitation has distinctive features of the supercritical Andronov--Hopf bifurcation and can be achieved by changing of a parameter value as well as by variation of initial conditions. Therefore the considered bifurcation is called Andronov-Hopf bifurcation with and without parameter.