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Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation

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  • Yihan Wang

    (School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia)

  • Jinjie Zhu

    (State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

Abstract

The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the phase sensitivity function in the spatial domain and time domain for oscillators close to saddle-node homoclinic (SNH) bifurcation, also known as saddle-node bifurcation on an invariant circle. It was found that the phase sensitivity function in the spatial domain can show the phase accumulation feature on the limit cycle, which can be ignored in the phase sensitivity function in the time domain. As an example, the synchronization distributions of uncoupled SNH oscillators driven by common and independent noises were investigated, where the space-dependent coupling function was considered on common noise. These results shed some light on the phase dynamics of oscillators close to bifurcations.

Suggested Citation

  • Yihan Wang & Jinjie Zhu, 2023. "Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation," Mathematics, MDPI, vol. 11(11), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2573-:d:1163555
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    References listed on IDEAS

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    1. Bashkirtseva, I.A. & Ryashko, L.B., 2004. "Stochastic sensitivity of 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 55-67.
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