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Novel transition and Bellerophon state in coupled Stuart–Landau oscillators |
Jia-Meng Zhang, Xue Li, Yong Zou, Shu-Guang Guan( ) |
| Department of Physics, East China Normal University, Shanghai 200241, China |
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Abstract We study synchronization in a system of Stuart–Landau oscillators with frequency-weighted coupling. For three typical unimodal frequency distributions, namely, the Lorentzian, the triangle, and the uniform, we found that the first-order transition occurs when the frequency distribution is relatively compact, while the synchronization transition is continuous when it is relatively wide. In both cases, there is a regime of Bellerophon state between the incoherent state and the synchronized state. Remarkably, we revealed novel transition behavior for such coupled oscillators with amplitudes, i.e., the regime of Bellerophon state actually contains two stages. In the first stage, the oscillators achieve chaotic phase synchronization; while in the second stage, oscillators form periodical phase synchronization. Our results suggest that Bellerophon state also exists in coupled oscillators with amplitude dynamics.
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| Keywords
synchronization
coupled oscillators
Stuart–Landau oscillators
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Corresponding Author(s):
Shu-Guang Guan
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Issue Date: 17 April 2019
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