Keep, break and breakout in food chains with two and three species

Maoxiang Wang; Fenglan Hu; Meng Xu; Zhipeng Qiu; Maoxiang Wang; Fenglan Hu; Meng Xu; Zhipeng Qiu

doi:10.3934/mbe.2021043

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 817-836. doi: 10.3934/mbe.2021043

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Research article

Keep, break and breakout in food chains with two and three species

School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

Received: 20 September 2020 Accepted: 07 December 2020 Published: 23 December 2020

In this paper, through Rosenzweig-MacArthur predator-prey model we study the cyclic coexistence and stationary coexistence and discuss temporal keep and break in the food chain with two species. Then species' diffusion is considered and its effect on oscillation and stability of the ODE system is studied concerning the two different states of coexistence. We find in cyclic coexistence temporal oscillation of population is translated into spatial oscillation although there is fluctuation at the beginning of population waves and finally more stable population evolution is observed. Furthermore, the presence of spatial diffusion of the species can lead to steady wavefront propagation and alter the population distribution in the food chain with two and three species. We show that lower-level species with slow propagation will limit higher-level species and help to keep food chain in space, but through fast propagation lower-level species can survive in a new space without predation and realize a breakout in the linear food chain.

Keywords:

Citation: Maoxiang Wang, Fenglan Hu, Meng Xu, Zhipeng Qiu. Keep, break and breakout in food chains with two and three species[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 817-836. doi: 10.3934/mbe.2021043

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Abstract

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