Forced synchronization of an oscillator with a line of equilibria

Korneev, Ivan A.; Slepnev, Andrei V.; Семенов, В. В.; Вадивасова, Т. Е.

doi:10.1140/epjst/e2020-900146-9

Cited by 10 publications

(3 citation statements)

References 30 publications

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“…Resultantly, a continuous dependence of the oscillation characteristics on the initial condition z 0 disappears. A similar character of the forgetting effect action was reported in earlier publications [18,17,19].…”

Section: Discussionsupporting

confidence: 87%

“…Thus, all the bifurcations of limit cycles exhibited by self-oscillators with one degree of freedom have been described in terms of oscillators with a line of equilibria. The similarity between classical self-oscillators and the considered systems with a line of equilibria is emphasized by the fact that undamped periodic oscillations in systems with a line of equilibria can be synchronized by external periodic forcing [18].…”

Section: Introductionmentioning

confidence: 99%

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Generalized model for steady-state bifurcations without parameters in memristor-based oscillators with lines of equilibria

Korneev¹,

Slepnev²,

Zakharova³

et al. 2022

Preprint

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We demonstrate how the pitchfork, transcritical and saddle-node bifurcations of steady states observed in dynamical systems with a finite number of isolated equilibrium points occur in systems with lines of equilibria. The exploration is carried out by using the numerical simulation and linear stability analysis applied to a model of a memristor-based oscillator. First, all the discussed bifurcation scenarios are considered in the context of systems including Chua's memristor with a piecewise-smooth characteristic. Then the memristor characteristic is changed to a function that is smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration. The presented results are obtained for electronic circuit models, but the considered bifurcation phenomena can be exhibited by systems with a line of equilibria of any nature.

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Section: Discussionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Generalized model for steady-state bifurcations without parameters in memristor-based oscillators with lines of equilibria

Korneev¹,

Slepnev²,

Zakharova³

et al. 2022

Preprint

Self Cite

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“…Thus, parallels between the bifurcation transitions in considered oscillators with a line of equilibria and self-oscillators with a finite number of isolated fixed points (for instance, the van der Pol self-oscillator) became visible. It has been uncovered that the oscillations in systems with a line of equilibria corresponding to motions along invariant closed curves can be synchronized by external periodic forcing 16 which increases the similarity. It allows to classify undamped periodic oscillations in autonomous systems with a line of equilibria as a special kind of selfsustained oscillations due to the possibility to observe the effect of frequency-phase locking.…”

Section: Introductionmentioning

confidence: 99%

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

Korneev,

Slepnev,

Vadivasova

et al. 2021

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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.

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