Subcritical Andronov-Hopf scenario for systems with a line of equilibria.
| Autor: | Korneev IA; Institute of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia., Slepnev AV; Institute of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia., Vadivasova TE; Institute of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia., Semenov VV; FEMTO-ST Institute/Optics Department, CNRS and University Bourgogne Franche-Comté, 15B avenue des Montboucons, Besançon Cedex 25030, France. |
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| Jazyk: | angličtina |
| Zdroj: | Chaos (Woodbury, N.Y.) [Chaos] 2021 Jul; Vol. 31 (7), pp. 073102. |
| DOI: | 10.1063/5.0050009 |
| Abstrakt: | Using numerical simulation methods and analytical approaches, 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. |
| Databáze: | MEDLINE |
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