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arXiv · 2103.04434

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

Ivan A. Korneev·Andrei V. Slepnev·Tatiana E. Vadivasova·Vladimir V. Semenov
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Abstract

Using numerical simulation methods and analytical approach, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.

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Ivan A. Korneev, Andrei V. Slepnev, Tatiana E. Vadivasova, Vladimir V. Semenov. 2021-04-30. Subcritical Andronov-Hopf scenario for systems with a line of equilibria. https://doi.org/10.1063/5.0050009

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