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Synchronization in the system of coupled non-identical non-isochronous Van fer Pol – Duffing oscillators with inertial and dissipative coupling is discussed. Generalized Adler's equation is obtained and investigated in the presence of all relevant factors affecting the synchronization (nonisochronism of the oscillators, their nonidentity, coupling of the… (More)

- Alexander P. Kuznetsov, Ludmila V. Turukina, Erik Mosekilde
- I. J. Bifurcation and Chaos
- 2001

Using the nonlinear dissipative kicked oscillator as an example, the correspondence between the descriptions provided by model dynamical systems of different classes is discussed. A detailed study of the approximate 1D map is undertaken: the period doubling is examined and the possibility of non-Feigenbaum period doubling is shown. Illustrations in the form… (More)

a r t i c l e i n f o a b s t r a c t We show that a hyperbolic chaos can be observed in resonantly coupled oscillators near a Hopf bifurcation, described by normal-form-type equations for complex amplitudes. The simplest example consists of four oscillators, comprising two alternatively activated, due to an external periodic modulation, pairs. In terms of… (More)

Features of synchronization picture in the system with the limit cycle embedded in a three-dimensional phase space are considered. By the example of Ressler system and Dmitriev-Kislov generator under the action of a periodic sequence of δ-function it is shown, that synchronization picture significantly depends on the direction of pulse action. Features of… (More)

- Alexander P. Kuznetsov, Ludmila V. Turukina, Nikolai Yu. Chernyshov, Yuliya V. Sedova
- I. J. Bifurcation and Chaos
- 2016

The phenomena of synchronization of oscillators are wide spread in nature and technology. A variety of examples can be found in electronics, laser physics, biophysics, chemistry, neuroscience, etc. [Pikovsky et al., 2001; Landa, 1996; Balanov et al., 2009; Kuramoto, 1984; Glass & Mackey, 1988; Winfree, 2001]. The synchronization in modern experiments for… (More)

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