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Pattern formation and parameter inversion for a discrete Lotka–Volterra cooperative system

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  • Xu, Li
  • Liu, Jiayi
  • Zhang, Guang

Abstract

In this paper, stability analysis is applied to a discrete Lotka–Volterra cooperative system with the periodic boundary conditions, then Turing pattern formation conditions can be derived, theory analysis and numerical simulation show that turing patterns can be realized. In addition, we also pay attention on what reason or what system environment to result into the current state patterns, which can be reduced to estimate or identify the system parameter. A regularization method is applied to parameter inversion, and numerical simulation can verify the effectiveness of the algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:226-231
    DOI: 10.1016/j.chaos.2018.03.035
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    References listed on IDEAS

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    1. Guin, Lakshmi Narayan, 2015. "Spatial patterns through Turing instability in a reaction–diffusion predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 174-185.
    2. Li Xu & Lianjun Zou & Zhongxiang Chang & Shanshan Lou & Xiangwei Peng & Guang Zhang, 2014. "Bifurcation in a Discrete Competition System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-7, April.
    3. 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.
    4. 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.
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    Cited by:

    1. Li, Tianhua & Zhang, Xuetian & Zhang, Chunrui, 2024. "Pattern dynamics analysis of a space–time discrete spruce budworm model," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

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