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Spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect

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  • Han, Renji
  • Dai, Binxiang

Abstract

Based on biological meaning, a kind of diffusive intraguild predation (IGP: resource, IG prey and IG predator) model with delay effect is investigated in this paper. The model has Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type II functional response between IG prey and IG predator. We first give sufficient conditions on the stability of possible nonnegative constant steady-state solutions for the proposed model, which give us a complete picture of the global dynamics. Then we investigate Hopf bifurcation near the unique positive constant steady-state solution by taking delay as bifurcation parameter and derive the Hopf bifurcation threshold. It is shown that the delay can induce three types of bistability (node-node bistability, node-cycle bistability and cycle-cycle bistability), periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive IGP model. Numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self-organised spatiotemporal patterns, which evolve from spiral patterns to irregular spatial patterns via spatiotemporal Hopf bifurcation. In addition, the impact of diffusion on the model’s dynamics under certain time delay are also explored.

Suggested Citation

  • Han, Renji & Dai, Binxiang, 2017. "Spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 177-201.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:177-201
    DOI: 10.1016/j.amc.2017.05.053
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    References listed on IDEAS

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    1. Tang, Xiaosong & Song, Yongli, 2015. "Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator–prey model with herd behavior," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 375-391.
    2. Jankovic, Masha & Petrovskii, Sergei & Banerjee, Malay, 2016. "Delay driven spatiotemporal chaos in single species population dynamics models," Theoretical Population Biology, Elsevier, vol. 110(C), pages 51-62.
    3. Zhao, Hongyong & Zhang, Xuebing & Huang, Xuanxuan, 2015. "Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 462-480.
    4. Shchekinova, Elena Y. & Löder, Martin G.J. & Boersma, Maarten & Wiltshire, Karen H., 2014. "Facilitation of intraguild prey by its intraguild predator in a three-species Lotka–Volterra model," Theoretical Population Biology, Elsevier, vol. 92(C), pages 55-61.
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    Cited by:

    1. Wu, Zeyan & Li, Jianjuan & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2019. "A spatial predator–prey system with non-renewable resources," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 381-391.

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