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Spatiotemporal dynamics analysis of a semi-discrete reaction-diffusion Mussel-Algae system with advection

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  • Zhong, Shihong
  • Xia, Juandi
  • Liu, Biao

Abstract

The spatiotemporal dynamics of a semi-discrete Mussel-Algae system with advection are investigated in this paper. The stability of equilibrium, the direction of Andronov-Hopf bifurcation and Bautin bifurcation to kinetic system are obtained via linear stability analysis, the Lyapunov coefficients and regularity. In order to analyze the Turing instability, the characteristic equations of the advection operator ∇ is considered. Combined with linear analysis, the critical condition of Turing instability conditions for advection term is obtained. Simulations are performed to illustrate the above theoretical results, such as bifurcation diagram, phase orbits and pattern formations. In addition, simulations for fixed parameters and special initial conditions indicate that the initial conditions can alter the structure of patterns. As a result, the theoretical results for Turing instability of some model with advection term may trigger some significance results for further research.

Suggested Citation

  • Zhong, Shihong & Xia, Juandi & Liu, Biao, 2021. "Spatiotemporal dynamics analysis of a semi-discrete reaction-diffusion Mussel-Algae system with advection," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006366
    DOI: 10.1016/j.chaos.2021.111282
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    References listed on IDEAS

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    1. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    2. Zhang, Guang & Zhang, Ruixuan & Yan, Yubin, 2020. "The diffusion-driven instability and complexity for a single-handed discrete Fisher equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    3. Li, Meifeng & Han, Bo & Xu, Li & Zhang, Guang, 2013. "Spiral patterns near Turing instability in a discrete reaction diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 1-6.
    4. Mai, F.X. & Qin, L.J. & Zhang, G., 2012. "Turing instability for a semi-discrete Gierer–Meinhardt system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2014-2022.
    5. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    6. Yang, Xiaofan & Yang, Maobin & Liu, Huaiyi & Liao, Xiaofeng, 2008. "Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 575-589.
    7. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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    Cited by:

    1. Chen, Mengxin & Wu, Ranchao, 2023. "Steady states and spatiotemporal evolution of a diffusive predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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