Geodesic
Synchronization self-sustained oscillators interacting through the memristor
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 26 (2018) no. 2, pp. 24-40.

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Aim. The aim of the paper is to study the mutual synchronization of two periodic selfsustained oscillators with a detuning of frequencies interacting through a memristor. It is supposed to give an answer to the question of the possibility of synchronization in this case and of its probable features. Method. The study is carried out by methods of theoretical analysis and computer simulation of oscillations in a system of two van der Pol oscillators interacting through a memristive conductivity. As the latter, an idealized Chua memristor is used. Results. It is shown that there is a line in the system phase space consisting of equilibrium points. This leads to specific properties of a synchronization. The phase-looking effect and the boundaries of the synchronization region with variation of the parameters depend on the initial conditions. A small perturbation of the equation describing the dynamics of the variable controlling the memristor leads to the disappearance of the equilibrium line and eliminates the dependence of the synchronization on the initial conditions. Discussion. In the mathematical model of self-sustained oscillators with a memristive connection, synchronization has essential features. However, the mathematical model is not rough, and in the real system these features should disappear. In this case, the consequence of the memristive connection can be long transient processes, depending on the initial state of the system.
Keywords: memristor, self-sustained oscillator, synchronization, phase-locking, line of equilibria. 
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     author = {I. A. Korneev and O. G. Shabalina and V. V. Semenov and T. E. Vadivasova},
     title = {Synchronization self-sustained oscillators interacting through the memristor},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {24--40},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2018_26_2_a2/}
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I. A. Korneev; O. G. Shabalina; V. V. Semenov; T. E. Vadivasova. Synchronization self-sustained oscillators interacting through the memristor. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 26 (2018) no. 2, pp. 24-40. http://geodesic.mathdoc.fr/item/IVP_2018_26_2_a2/