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

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.

arXiv comment3 figures. arXiv admin note: substantial text overlap with arXiv:1705.06301

References in corpus (4)

• Memcomputing: a computing paradigm to store and process information on the same physical platform
• Stochastic memory: memory enhancement due to noise
• Synchronization of two memristive coupled van der Pol oscillators
• Experimental evidence of chaos from memristors

Cited by in corpus (4)

• Forced synchronization of an oscillator with a line of equilibria
• Subcritical Andronov-Hopf scenario for systems with a line of equilibria
• Quantum effects in graphitic materials: Colossal magnetoresistance, Andreev reflections, Little-Parks effect, ferromagnetism, and granular superconductivity
• Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria