Self-organized partially synchronous dynamics in populations of nonlinearly coupled oscillators |
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Authors: | Arkady Pikovsky |
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Institution: | Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Street 24/25, D-14476 Potsdam-Golm, Germany |
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Abstract: | We analyze a minimal model of a population of identical oscillators with a nonlinear coupling—a generalization of the popular Kuramoto model. In addition to well-known for the Kuramoto model regimes of full synchrony, full asynchrony, and integrable neutral quasiperiodic states, ensembles of nonlinearly coupled oscillators demonstrate two novel nontrivial types of partially synchronized dynamics: self-organized bunch states and self-organized quasiperiodic dynamics. The analysis based on the Watanabe-Strogatz ansatz allows us to describe the self-organized bunch states in any finite ensemble as a set of equilibria, and the self-organized quasiperiodicity as a two-frequency quasiperiodic regime. An analytic solution in the thermodynamic limit of infinitely many oscillators is also discussed. |
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Keywords: | 05 45 Xt 05 65 +b |
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