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Spiral patterns near Turing instability in a discrete reaction diffusion system

Author

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  • Li, Meifeng
  • Han, Bo
  • Xu, Li
  • Zhang, Guang

Abstract

In this paper, linear stability analysis is applied to an exponential discrete Lotka–Volterra system, which describes the competition between two identical species. Conditions for the Turing instability are obtained and the emergence of spiral patterns is demonstrated by means of numerical simulations in the vicinity of the bifurcation point. Moreover, the impact of crucial system parameters on the stability and coherence of spiral patterns is illustrated on several examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:49:y:2013:i:c:p:1-6
    DOI: 10.1016/j.chaos.2013.01.010
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    References listed on IDEAS

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    1. Perc, Matjaž, 2007. "Spatial coherence resonance in neuronal media with discrete local dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 64-69.
    2. Wang, Weiming & Zhang, Lei & Wang, Hailing & Li, Zhenqing, 2010. "Pattern formation of a predator–prey system with Ivlev-type functional response," Ecological Modelling, Elsevier, vol. 221(2), pages 131-140.
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    Cited by:

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    2. Flores, J.C., 2020. "Game theory approach to sterile release populations and replicator dynamics: Niche fragmentation and resilience," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Matvey Kulakov & Efim Frisman, 2023. "Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    4. Xu, Li & Liu, Jiayi & Zhang, Guang, 2018. "Pattern formation and parameter inversion for a discrete Lotka–Volterra cooperative system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 226-231.
    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. Han, Xiaoling & Lei, Ceyu, 2023. "Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    7. Ghosh, Joydev & Sahoo, Banshidhar & Poria, Swarup, 2017. "Prey-predator dynamics with prey refuge providing additional food to predator," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 110-119.
    8. Zhang, Yin & Wu, Fuqiang & Wang, Chunni & Ma, Jun, 2019. "Stability of target waves in excitable media under electromagnetic induction and radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 519-530.

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