Subcritical Andronov-Hopf scenario for systems with a line of equilibria

Abstract

Hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space is analyzed. The demonstrated bifurcation phenomena correspond to a self-oscillation excitation mechanism being equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. Hysteresis and bistability accompanying the discussed processes are shown and explained. The study is carried out on an example of a nonlinear memristor-based self-oscillator. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored by means of numerical modelling and analytical solution. Then the memristor characteristic is changed to a function being smooth everywhere in order to demonstrate that the observed effects are not associated with the smoothness of the memristor model. Finally, the action of the memristor forgetting effect is taken into consideration.