Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos
https://doi.org/10.18255/1818-1015-2015-5-595-608
Abstract
We consider a finite-dimensional model of phase oscillators with inertia in the case of star configuration of coupling. The system of equations is reduced to a nonlinearly coupled system of pendulum equations. We prove that the transition from synchronous to asynchronous oscillations occurs via bifurcation of saddle-node equilibrium. In this connection the asynchronous regime can be partially synchronous rotations. We find that the reverse transition from asynchronous to synchronous regime occurs via bifurcation of homoclinic orbit both of the saddle equilibrium point and of the saddle periodic orbit. In the case of homoclinic loop of the saddle point the synchrony appears only from asynchronous mode without partially synchronized rotations. In the case of the homoclinic curve of the saddle periodic orbit the system undergoes a chaotic rotation regime which results in a random return to synchrony. We establish that return transitions are hysteretic in the case of large inertia.
About the Authors
V. N. Belykh
Nizhny Novgorod University, Gagarin Ave., 23, Nizhny Novgorod, 603950, Russia, Volga State University of Water Transport, Nesterova str., 5, Nizhny Novgorod, 603950, Russia
Russian Federation
Department of Control Theory
Russian Federation
Department of Control Theory
M. I. Bolotov
Nizhny Novgorod University, Gagarin Ave., 23, Nizhny Novgorod, 603950, Russia
Russian Federation
Department of Control Theory
Russian Federation
Department of Control Theory
G. V. Osipov
Nizhny Novgorod University, Gagarin Ave., 23, Nizhny Novgorod, 603950, Russia
Russian Federation
Department of Control Theory
Russian Federation
Department of Control Theory
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Review
For citations:
Belykh V.N., Bolotov M.I., Osipov G.V. Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos. Modeling and Analysis of Information Systems. 2015;22(5):595-608. (In Russ.) https://doi.org/10.18255/1818-1015-2015-5-595-608
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