Forced synchronization of an oscillator with a line of equilibria
- PDF / 628,928 Bytes
- 10 Pages / 481.89 x 708.661 pts Page_size
- 22 Downloads / 196 Views
part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-900146-9
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Forced synchronization of an oscillator with a line of equilibria Ivan A. Korneev1 , Andrei V. Slepnev1 , Vladimir V. Semenov2,a , and Tatiana E. Vadivasova1 1
2
Department of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia FEMTO-ST Institute/Optics Department, CNRS & University Bourgogne FrancheComt´e, 15B avenue des Montboucons, Besan¸con Cedex 25030, France Received 18 July 2019 / Accepted 8 June 2020 Published online 28 September 2020 Abstract. The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodic force is combined with a theoretical analysis by means of the quasi-harmonic reduction. Both two mechanisms of synchronization are demonstrated: phase and frequency locking and suppression by an external signal. Classification of undamped oscillations in an autonomous system with a line of equilibria as a special kind of self-sustained oscillations is concluded due to the possibility to observe the effect of frequency-phase locking in the same system in the presence of an external influence. It is established that the occurrence of phase locking in the considered system continuously depends both on parameter values and initial conditions. The simultaneous dependence of synchronization area boundaries on the initial conditions and the parameter values is also shown.
1 Introduction The effect of synchronization first described in 1665 by C. Huygens [1] represents a fundamental property of dynamical systems [2–4]. The synchronization associated with frequency and phase locking (the synchronization in the sense of Huygens) is a significant feature of self-oscillatory systems. Depending on specifics of explored objects the synchronization can be exhibited in a different manner. Thus, stochastic synchronization [5–9], synchronization of chaos [10–12], lag synchronization [13], generalized synchronization [14,15] are distinguished besides the classical forms of mutual and forced synchronization. The phenomenon of synchronization is not limited to nonlinear dissipative systems with a finite number of attractors, but also applies to Hamiltonian systems [16–18]. Despite synchronization is well-studied for different kinds of dynamical systems, there exists a class of dissipative dynamical systems for which this effect has not been researched in terms of the Huygens treatment of phase-frequency locking. Such systems are oscillators with m-dimensional manifolds of equilibria which consist of a
e-mail: [email protected]
2216
The European Physical Journal Special Topics
non-isolated equilibrium points. In the simplest case these manifolds exist as a line of equilibria (m = 1). Normally hyperbolic manifolds of equilibria are distinguished and their equilibria are characterized by m purely imagine or zero eigenvalues, whereas all the other eigenvalues ha
Data Loading...
