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Spiral dynamics in oscillatory bilayer systems with an inhomogeneous inter-layer coupling

Author

Listed:
  • Zhang, Yiling
  • Yuan, Guoyong
  • Liu, Jun
  • Shi, Jifang
  • Wang, Guangrui
  • Chen, Shaoying

Abstract

Spiral dynamics in the oscillatory bilayer system with an inhomogeneous inter-layer coupling and a spiral-resting initial state are studied, where the square coupled patches are arranged into a square lattice array. Depending on the patch side length, the lattice space and the coupling strength, different dynamical behaviors can be observed. The complete synchronization of two spiral waves easily occurs when the coupled areas occupy a larger proportion in the whole region. The bilayer system can also show several typical asynchronous patterns, where the spiral with the closed tip path, the spiral with the complex phase shifting, the state with multiple spirals, the spiral turbulence, and the non-smooth traveling pulses can be formed in the single layers of the bilayer. The variable difference functions are computed, and three types of asymptotic behaviors are identified, which include the behaviors of approaching the constant, periodic variation, and aperiodic variation around the constant. These asymptotic behaviors can describe some properties of the bilayer patterns after a transient interval. For example, the variable difference function has a periodical asymptotic behavior when the spiral with the closed tip path is formed in the single layer. The heterogeneity of inter-layer coupling can also induce some complex tip trajectories.

Suggested Citation

  • Zhang, Yiling & Yuan, Guoyong & Liu, Jun & Shi, Jifang & Wang, Guangrui & Chen, Shaoying, 2023. "Spiral dynamics in oscillatory bilayer systems with an inhomogeneous inter-layer coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    • Handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123007835
    DOI: 10.1016/j.physa.2023.129228
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    References listed on IDEAS

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    1. Ma, Jun & Gao, Ji-Hua & Wang, Chun-Ni & Su, Jun-Yan, 2008. "Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 521-530.
    2. Etémé, A.S. & Tabi, C.B. & Mohamadou, A. & Kofané, T.C., 2019. "Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    3. Guo, Shuangjian & Dai, Qionglin & Cheng, Hongyan & Li, Haihong & Xie, Fagen & Yang, Junzhong, 2018. "Spiral wave chimera in two-dimensional nonlocally coupled Fitzhugh–Nagumo systems," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 394-399.
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