Frequency mismatch induces Bellerophon state and mixed explosive synchronization in a two-dimensional lattice

We study synchronization of coupled phase oscillators with linear natural frequencies in a two-dimensional lattice. The effects of two typical frequency layouts on synchronization dynamics are analyzed and discussed. The results show that the two typical frequency layouts induce two interesting dyna...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2019-08, Vol.92 (8), p.1-7, Article 177
Main Authors: Zhu, Liu-Hua, Yuan, Wu-Jie
Format: Article
Language:English
Subjects:
Complex Systems
Condensed Matter Physics
Fluid- and Aerodynamics
Layouts
Oscillators
Phase transitions
Physics
Physics and Astronomy
Regular Article
Resonant frequencies
Solid State Physics
Synchronism
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Summary:We study synchronization of coupled phase oscillators with linear natural frequencies in a two-dimensional lattice. The effects of two typical frequency layouts on synchronization dynamics are analyzed and discussed. The results show that the two typical frequency layouts induce two interesting dynamical behaviors. One is the Bellerophon state, the other is a mixed explosive synchronization. The Bellerophon state is a transitional state between the incoherent state and the π state, in which neither the instantaneous phases nor the instantaneous frequencies of the oscillators are locked. But the oscillators split into a series of discrete clusters and each cluster shares a unique effective frequency. The mixed explosive synchronization means that the synchronization transition is not a sudden jump, but always accompanied with continuous phase transitions. Our current work may provide a new insight into understanding of the Bellerophon state and the mixed explosive synchronization in homogenous networks. Graphical abstract
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2019-100203-2