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Delay-induced self-organization dynamics in a prey-predator network with diffusion

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Abstract

Considering that time delay (delay) is a common phenomenon in biological systems, reaction-diffusion equations with delay are widely used to study the dynamic mechanism of those systems, in which delay can induce the loss of stability and degradation of performance. In this paper, taking into account the inhomogeneous distribution of species in space and this can be considered as a random network, the pattern dynamics of a prey-predator network system with diffusion and delay are investigated. The effect of delay and diffusion on the network system is obtained by linear stability analysis, including the stability and Hopf bifurcation as well as Turing pattern. Our results show that the stability of the system changes with the value of delay. Moreover, we obtain Turing pattern related to the network connection probability and diffusion. Finally, the numerical simulation verifies our results.

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Acknowledgements

The authors would particularly like to thank the anonymous referee and Prof.Yong Xu for their comments.

Funding

Funding was provided by National Natural Science Foundation of China (11772291), Basic research Project of Universities in Henan Province (21zx009).

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Authors and Affiliations

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China

    Qing Hu & Jianwei Shen

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  1. Qing Hu
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  2. Jianwei Shen
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Correspondence to Jianwei Shen.

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Hu, Q., Shen, J. Delay-induced self-organization dynamics in a prey-predator network with diffusion. Nonlinear Dyn 108, 4499–4510 (2022). https://doi.org/10.1007/s11071-022-07431-5

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