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Hamdallah, S.A.A. and Arafa, A.A. (2023) Stability Analysis of Filippov Prey–predator Model with Fear Effect and Prey Refuge. Journal of Applied Mathematics and Computing, 70, 73-102.
https://doi.org/10.1007/s12190-023-01934-z

has been cited by the following article:

• TITLE: Dynamical Behaviors of a Modified Leslie-Gower Predator-Prey System with Fear Effect and Prey Refuge

  AUTHORS: Ke Yuan

  KEYWORDS: Fear Effect, Prey Refuge, Predator-Taxis Sensitivity, Population Density, Stability

  JOURNAL NAME: Open Journal of Modelling and Simulation, Vol.12 No.4, October 25, 2024

  ABSTRACT: In this paper, the dynamical behaviors of a modified Leslie-Gower predator-prey model incorporating fear effect and prey refuge are investigated. We delve into the construction of the model and its biological significance, with preliminary results encompassing positivity, boundedness, and persistence. The stability of the system’s boundary and positive equilibrium points is proven by calculating the real part of the eigenvalues of the Jacobian matrix. At the positive equilibrium point, we demonstrate that the system’s unique positive equilibrium is globally asymptotically stable by using the Dulac criterion. Furthermore, at this equilibrium point, we employ the Implicit Function Theorem to discuss how fear effects and prey refuges influence the population densities of both prey and predators. Finally, numerical simulations are conducted to validate the above-mentioned conclusions and explored the impact of Predator-taxis sensitivity α on dynamics of the system.