Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos
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 bifurc...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-10-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/280 |
| _version_ | 1797877917226631168 |
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| author | V. N. Belykh M. I. Bolotov G. V. Osipov |
| author_facet | V. N. Belykh M. I. Bolotov G. V. Osipov |
| author_sort | V. N. Belykh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T02:24:28Z |
| format | Article |
| id | doaj.art-fa388a91193440fc98ef61776b239912 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:24:28Z |
| publishDate | 2015-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-fa388a91193440fc98ef61776b2399122023-03-13T08:07:34ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-10-0122559560810.18255/1818-1015-2015-5-595-608261Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of ChaosV. N. Belykh0M. I. Bolotov1G. V. Osipov2Нижегородский государственный университет им. Н.И. Лобачевского, пр. Гагарина, 23, Нижний Новгород, 603950, Россия Волжский государственный университет водного транспорта, ул. Нестерова, 5, Нижний Новгород, 603950, РоссияНижегородский государственный университет им. Н.И. Лобачевского, пр. Гагарина, 23, Нижний Новгород, 603950, Россия,Нижегородский государственный университет им. Н.И. Лобачевского, пр. Гагарина, 23, Нижний Новгород, 603950, РоссиWe 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.https://www.mais-journal.ru/jour/article/view/280осцилляторысинхронизациямаятникзвезда |
| spellingShingle | V. N. Belykh M. I. Bolotov G. V. Osipov Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos Моделирование и анализ информационных систем осцилляторы синхронизация маятник звезда |
| title | Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos |
| title_full | Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos |
| title_fullStr | Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos |
| title_full_unstemmed | Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos |
| title_short | Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos |
| title_sort | kuramoto phase model with inertia bifurcations leading to the loss of synchrony and to the emergence of chaos |
| topic | осцилляторы синхронизация маятник звезда |
| url | https://www.mais-journal.ru/jour/article/view/280 |
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