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Turing patterns in a predator–prey model on complex networks

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Abstract

Predator–prey model with modified Leslie–Gower and Holling type III schemes governed by reaction–diffusion equations can exhibit diversified pattern formations. Considering that species are usually organized as networks instead of being continuously distributed in space, it is essential to study predator–prey system on complex networks. There are the close relation to discrete predator–prey system and continuous version. Here, we extend predator–prey system from continuous media to random networks via finite volume method. With the help of linear stability analysis, Turing patterns of the Leslie–Gower Holling type III predator–prey model on several different networks are investigated. By contrasting and analyzing numerical simulations, we study the influences of network type, average degree as well as diffusion rate on pattern formations.

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Acknowledgements

This study was funded by the National Natural Science Foundation of China (grant numbers 31700393, 11701348), the China Postdoctoral Science Foundation (project 2018T111091) and Key Area R&D Program of Shannxi Province (No. 2019ZDLGY17-07).

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Authors and Affiliations

  1. Center for Ecology and Environmental Sciences, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Chen Liu

  2. Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China

    Lili Chang

  3. Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang, 110016, Liaoning, China

    Yue Huang

  4. Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Zhen Wang

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  1. Chen Liu
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  2. Lili Chang
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  3. Yue Huang
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  4. Zhen Wang
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Correspondence to Lili Chang.

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Liu, C., Chang, L., Huang, Y. et al. Turing patterns in a predator–prey model on complex networks. Nonlinear Dyn 99, 3313–3322 (2020). https://doi.org/10.1007/s11071-019-05460-1

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  • DOI: https://doi.org/10.1007/s11071-019-05460-1

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