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Graph-theoretic method on the periodicity of coupled predator–prey systems with infinite delays on a dispersal network

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  • Zhang, Chunmei
  • Shi, Lin

Abstract

In this paper, infinite delays and prey dispersal on a network are considered in multi-patch periodic predator–prey systems. Novel graph-theoretic method is adopted to estimate the uniform upper bounds of unknown solutions to operator equation Lu=λNu. The existence criterion of positive periodic solutions to coupled predator–prey systems is obtained by using classic coincidence degree theory, which is closely related to prey dispersal network in a patch environment. Finally, two numerical examples are also shown to illustrate the effectiveness of theoretical results.

Suggested Citation

  • Zhang, Chunmei & Shi, Lin, 2021. "Graph-theoretic method on the periodicity of coupled predator–prey systems with infinite delays on a dispersal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    • Handle: RePEc:eee:phsmap:v:561:y:2021:i:c:s0378437120306634
    DOI: 10.1016/j.physa.2020.125255
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    References listed on IDEAS

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    1. Zhang, Chunmei & Han, Bang-Sheng, 2020. "Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Zhang, Xinhong & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2016. "Periodic solutions and stationary distribution of mutualism models in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 270-282.
    3. Anjos, Lucas dos & Costa, Michel Iskin da S. & Almeida, Regina C., 2020. "Characterizing the existence of hydra effect in spatial predator-prey models and the influence of functional response types and species dispersal," Ecological Modelling, Elsevier, vol. 428(C).
    4. Jiang, Daqing & Zuo, Wenjie & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Stationary distribution and periodic solutions for stochastic Holling–Leslie predator–prey systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 16-28.
    5. Zhang, Yan & Chen, Shihua & Gao, Shujing & Wei, Xiang, 2017. "Stochastic periodic solution for a perturbed non-autonomous predator–prey model with generalized nonlinear harvesting and impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 347-366.
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    Cited by:

    1. Singha, Joydeep & Ramaswamy, Ramakrishna, 2022. "Phase-locking in k-partite networks of delay-coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Gao, Shang & Peng, Keyu & Zhang, Chunrui, 2021. "Existence and global exponential stability of periodic solutions for feedback control complex dynamical networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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