Abstract:
We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott – Antonsen approach, the problem is formulated as a system of partial derivative equations for the local complex order parameter. In this framework, we investigate the existence and stability of twisted states. Both fully coherent and partially coherent stable twisted states were found (the latter ones for the first time for identical oscillators). We show that twisted states can be stable starting from a certain critical value of the medium length, or on a length segment. The analytical results are confirmed with direct numerical simulations in finite ensembles.
Citation:
Dmitry Bolotov, Maxim Bolotov, Lev Smirnov, Grigory Osipov, Arkady Pikovsky, “Twisted States in a System of Nonlinearly Coupled Phase Oscillators”, Regul. Chaotic Dyn., 24:6 (2019), 717–724
\Bibitem{BolBolSmi19}
\by Dmitry Bolotov, Maxim Bolotov, Lev Smirnov, Grigory Osipov, Arkady Pikovsky
\paper Twisted States in a System of Nonlinearly Coupled Phase Oscillators
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 6
\pages 717--724
\mathnet{http://mi.mathnet.ru/rcd1035}
\crossref{https://doi.org/10.1134/S1560354719060091}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85076350324}
Linking options:
https://www.mathnet.ru/eng/rcd1035
https://www.mathnet.ru/eng/rcd/v24/i6/p717
This publication is cited in the following 11 articles:
L A Smirnov, M I Bolotov, A Pikovsky, “Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators”, J. Phys. Complex., 5:1 (2024), 015019
Yong-Hyok An, Myong-Su Ho, Ryong-Son Kim, Chol-Ung Choe, “Stability of the twisted states in a ring of oscillators interacting with distance-dependent delays”, Physica D: Nonlinear Phenomena, 464 (2024), 134204
Christian Bick, Tobias Böhle, Oleh E Omel'chenko, “Hopf bifurcations of twisted states in phase oscillators rings with nonpairwise higher-order interactions”, J. Phys. Complex., 5:2 (2024), 025026
Jin-Song Kang, Yong-Hyok An, Ryong-Son Kim, Chol-Ung Choe, “Periodic external driving of transmission-delay-coupled phase oscillator system: Switching between different twisted states”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:12 (2024)
Hao-jie Luo, Yu Xue, Mu-yang Huang, Yi Wang, Qiang Zhang, Kun Zhang, “Turing patterns on coupled phase oscillator chains with localized many-body interactions”, EPL, 142:4 (2023), 41002
D. I. Bolotov, M. I. Bolotov, L. A. Smirnov, G. V. Osipov, A. S. Pikovsky, “Synchronization Regimes in an Ensemble of Phase Oscillators Coupled Through a Diffusion Field”, Radiophys Quantum El, 64:10 (2022), 709
Seungjae Lee, Katharina Krischer, “Nontrivial twisted states in nonlocally coupled Stuart-Landau oscillators”, Phys. Rev. E, 106:4 (2022)
M. Goebel, M. S. Mizuhara, S. Stepanoff, “Stability of twisted states on lattices of Kuramoto oscillators”, Chaos, 31:10 (2021), 103106
D. A. Safonov, V. K. Vanag, “Oscillatory microcells connected on a ring by chemical waves”, Chaos, 31:6 (2021), 063134
M. I. Bolotov, L. A. Smirnov, E. S. Bubnova, G. V. Osipov, A. S. Pikovsky, “Spatiotemporal regimes in the Kuramoto-Battogtokh system of nonidentical oscillators”, J. Exp. Theor. Phys., 132:1 (2021), 127–147
Y. Kawamura, “Stable plane waves in nonlocally coupled phase oscillators”, AIP Adv., 11:1 (2021), 015304
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