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A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments

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  • Zhang, Shengqiang
  • Yuan, Sanling
  • Zhang, Tonghua

Abstract

In this paper, we formulate a stage-structured predator-prey model with Holling-I and Crowley-Martin functional responses in deterministic and stochastic environments, where Holling-I and Crowley-Martin functional responses conform respectively to predator feeds on juvenile and adult prey. In the deterministic case, by discussing the existence and stability of equilibria as well as equilibrium point bifurcations, we observe that the model can possess more than one positive equilibrium and exhibit rich dynamics such as bistability and complex bifurcations, meaning that its dynamics is easily affected by the environmental perturbations. In the stochastic case, by constructing appropriate Lyapunov functions we establish respectively the sufficient conditions for the ergodic stationary distribution and extinction of the model. Moreover, for the bistability scenario between a positive equilibrium and an interior limit cycle in the absence of noise, we can numerically observe the phenomenon of noise-induced state frequent switching between two stochastic attractors in the bistable zone. Biologically, our results can partially explain the phenomenon that in real world, for the inevitably small environmental noise intensities, the biological populations may remain at least two patterns of survival to switch.

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  • Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321006822
    DOI: 10.1016/j.amc.2021.126598
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    References listed on IDEAS

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    1. Meng, Xin-You & Huo, Hai-Feng & Xiang, Hong & Yin, Qi-yu, 2014. "Stability in a predator–prey model with Crowley–Martin function and stage structure for prey," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 810-819.
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    7. Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
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    1. Liang, Ziwei & Meng, Xinyou, 2023. "Stability and Hopf bifurcation of a multiple delayed predator–prey system with fear effect, prey refuge and Crowley–Martin function," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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