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Permanency in predator–prey models of Leslie type with ratio-dependent simplified Holling type-IV functional response

Author

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  • Amirabad, H. Qolizadeh
  • RabieiMotlagh, O.
  • MohammadiNejad, H.M.

Abstract

We consider a predator–prey model of Leslie type with ratio-dependent simplified Holling type-IV functional response. The novelty of the model is that the functional response simulates group defense of the prey kind, which in turn, affects permanency of the system and existence of limit cycles. We show that permanency of the system holds automatically for some values of parameters and provides sufficient conditions for global stability of interior equilibrium by constructing a Lyapunov function. We prove that for some values of parameters the system exhibits a Hopf cycle and provides conditions by which the corresponding stable Hopf cycle is the only cycle that model may have. Numerical simulations show that if the conditions are broken, the model may have more than one limit cycle, which is phenomenal among the predator–prey models with one interior equilibrium.

Suggested Citation

  • Amirabad, H. Qolizadeh & RabieiMotlagh, O. & MohammadiNejad, H.M., 2019. "Permanency in predator–prey models of Leslie type with ratio-dependent simplified Holling type-IV functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 63-76.
    • Handle: RePEc:eee:matcom:v:157:y:2019:i:c:p:63-76
    DOI: 10.1016/j.matcom.2018.09.023
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    Cited by:

    1. Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    2. Luyao Lv & Xianyi Li, 2024. "Stability and Bifurcation Analysis in a Discrete Predator–Prey System of Leslie Type with Radio-Dependent Simplified Holling Type IV Functional Response," Mathematics, MDPI, vol. 12(12), pages 1-16, June.

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