5a, Nesterov st., Nizhny Novgorod, 603600, Russia
Volga State Academy of Water Transport, Mathematics Department
Belykh V. N., Petrov V. S., Osipov G. V.
Dynamics of the Finite-dimensional Kuramoto Model: Global and Cluster Synchronization
2015, vol. 20, no. 1, pp. 37-48
Synchronization phenomena in networks of globally coupled non-identical oscillators have been one of the key problems in nonlinear dynamics over the years. The main model used within this framework is the Kuramoto model. This model shows three main types of behavior: global synchronization, cluster synchronization including chimera states and totally incoherent behavior. We present new sufficient conditions for phase synchronization and conditions for an asynchronous mode in the finite-size Kuramoto model. In order to find these conditions for constant and time varying frequency mismatch, we propose a simple method of comparison which allows one to obtain an explicit estimate of the phase synchronization range. Theoretical results are supported by numerical simulations.
Belykh V. N., Pankratova E. V.
Chaotic dynamics of two Van der Pol–Duffing oscillators with Huygens coupling
2010, vol. 15, no. 2-3, pp. 274-284
We consider a system of two coupled Van der Pol-Duffing oscillators with Huygens coupling as an appropriate model of two mechanical oscillators connected to a movable platform via a spring. We examine the complicated dynamics of the system and study its multistable behavior. In particular, we reveal the co-existence of several chaotic regimes and study the structure of the associated riddled basins.