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Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment

Qi, Haokun ; Meng, Xinzhu ; Hayat, Tasawar ; Hobiny, Aatef

Mathematical methods in the applied sciences, 2022-07, Vol.45 (10), p.6217-6254 [Periódico revisado por pares]

Freiburg: Wiley Subscription Services, Inc

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  • Título:
    Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment
  • Autor: Qi, Haokun ; Meng, Xinzhu ; Hayat, Tasawar ; Hobiny, Aatef
  • Assuntos: Bifurcation theory ; Diffusion effects ; Diffusion rate ; Eigenvalues ; Fear ; fear effect ; Hopf bifurcation ; Mathematical models ; Parameters ; Populations ; positive steady states ; Predator-prey simulation ; Predators ; predator‐poisoned ; reaction–diffusion predator–prey model ; Stability analysis ; Steady state ; steady state bifurcation
  • É parte de: Mathematical methods in the applied sciences, 2022-07, Vol.45 (10), p.6217-6254
  • Descrição: In this paper, we propose a reaction–diffusion predator–prey model with fear effect under a predator‐poisoned environment. First, we analyze the existence and stability of constant positive steady states. Second, taking the cost of minimum fear as the bifurcation parameter, the direction and stability of spatially homogeneous/inhomogeneous periodic solutions are investigated. Then, some properties of nonconstant positive steady states are investigated, such as nonexistence, existence, and steady state bifurcation. Applying the fixed point index theory, the existence of the nonconstant positive steady state is discussed, indicating that the proper diffusion rate of prey and larger diffusion rate of predator are beneficial to survival of populations. Moreover, taking the diffusion rate of predator as the bifurcation parameter, the steady state bifurcations from simple and double eigenvalues are intensively established. At last, the validity of the theoretical analysis is verified by numerical simulations. Biological interpretation reveals that the fear effect and the diffusion rate of populations can lead to the emergence of Hopf and steady state bifurcation, thereby destroying the stability of populations and promoting the benign evolution of populations.
  • Editor: Freiburg: Wiley Subscription Services, Inc
  • Idioma: Inglês
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