In this study, we investigated the impact of the asymmetry of a coupling scheme on oscillator dynamics in a star network. We obtained stability conditions for the collective behavior of the systems, ranging from an equilibrium point over complete synchronization (CS) and quenched hub incoherence to remote synchronization states using both numerical and analytical methods. The coupling asymmetry factor α significantly influences and determines the stable parameter region of each state. For α ≠ 1, the equilibrium point can emerge when the Hopf bifurcation parameter a is positive, which is impossible for diffusive coupling. However, CS can occur even if a is negative under α < 1. Unlike diffusive coupling, we observe more behavior when α ≠ 1, including additional in-phase remote synchronization. These results are supported by theoretical analysis and validated through numerical simulations and independent of network size. The findings may offer practical methods for controlling, restoring, or obstructing specific collective behavior.
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April 2023
Research Article|
April 10 2023
Collective behavior of identical Stuart–Landau oscillators in a star network with coupling asymmetry effects
XinYue Chen;
XinYue Chen
(Data curation, Software, Writing – original draft)
College of Science, Northwest A&F University
, Yangling 712100, China
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Ran Chen;
Ran Chen
(Visualization, Writing – review & editing)
College of Science, Northwest A&F University
, Yangling 712100, China
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YiLin Sun;
YiLin Sun
(Visualization, Writing – review & editing)
College of Science, Northwest A&F University
, Yangling 712100, China
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Shuai Liu
Shuai Liu
a)
(Conceptualization, Methodology, Validation, Writing – review & editing)
College of Science, Northwest A&F University
, Yangling 712100, China
a)Author to whom correspondence should be addressed: liushuai0109@mails.ucas.ac.cn
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a)Author to whom correspondence should be addressed: liushuai0109@mails.ucas.ac.cn
Chaos 33, 043117 (2023)
Article history
Received:
January 18 2023
Accepted:
March 22 2023
Citation
XinYue Chen, Ran Chen, YiLin Sun, Shuai Liu; Collective behavior of identical Stuart–Landau oscillators in a star network with coupling asymmetry effects. Chaos 1 April 2023; 33 (4): 043117. https://doi.org/10.1063/5.0142904
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