A delay-induced predator–prey model with Holling type functional response and habitat complexity

Ma, Zhihui; Wang, Shufan

doi:10.1007/s11071-018-4274-2

Cited by 38 publications

(15 citation statements)

References 43 publications

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“…In [24], the author introduced habitat complexity into the ordinary differential equation system with Holling type functional response function and delay. The model is as follows:…”

Section: Establishment Of the Modelmentioning

confidence: 99%

Time-delay effect on a diffusive predator–prey model with habitat complexity

Liu

Yang

2021

Adv Differ Equ

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Based on the predator–prey system with a Holling type functional response function, a diffusive predator–prey system with digest delay and habitat complexity is proposed. Firstly, the stability of the equilibrium of diffusion system without delay is studied. Secondly, under the Neumann boundary conditions, taking time delay as the bifurcation parameter, by analyzing the eigenvalues of linearized operator of the system and using the normal form theory and center manifold method of partial functional differential equations, the effect of time delay on the stability of the system is studied and the conditions under which Hopf bifurcation occurs are given. In addition, the calculation formulas of the bifurcation direction and the stability of bifurcating periodic solutions are derived. Finally, the accuracy of theoretical analysis results is verified by numerical simulations and the biological explanation is given for the analysis results.

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“…In [24], the author introduced habitat complexity into the ordinary differential equation system with Holling type functional response function and delay. The model is as follows:…”

Section: Establishment Of the Modelmentioning

confidence: 99%

Time-delay effect on a diffusive predator–prey model with habitat complexity

Liu

Yang

2021

Adv Differ Equ

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“…The homogeneous Neumann boundary conditions represents that the prey and the predator move with a distance between 0 and lπ. For more examples see [8,11,18,22]. It is easy to check that the homogeneous steady states of the system (1.4) are (0, 0), (k, 0) and (u * , v * ) where…”

Section: )mentioning

confidence: 99%

Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping

Souna

Djilali

Charif

2020

Math. Model. Nat. Phenom.

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In this paper, we consider a new approach of prey escaping from herd in a predator-prey model with the presence of spatial diffusion. First, the sensitivity of the equilibrium state density with respect to the escaping rate has been studied. Then, the analysis of the non diffusive system was investigated where boundedness, local, global stability, Hopf bifurcation are obtained. Besides, for the diffusive system, we proved the occurrence of Hopf bifurcation and the non existence of diffusion driven instability. Furthermore, the direction of Hopf bifurcation has been proved using the normal form on the center manifold. Some numerical simulations have been used to illustrate the obtained results.

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“…Many studies have shown that habitat complexity has a stabilizing effect on the predator-prey model [4][5][6]. In [8], Z. Ma and S. Wang studied a predator-prey model with habitat complexity and time delay, that is…”

Section: Introductionmentioning

confidence: 99%

“…If α = 1 (α = 2), the functional response is Holling type I (II). In [8], Z. Ma and S. Wang studied the positivity, boundedness, stability, and Hopf bifurcation of the model (1.1). They observed the stabilizing and destabilizing effects of habitat complexity and periodic oscillation caused by time delay under some parameters.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics Induced by Nonlocal Competition in a Diffusion Predator-Prey System with Habitat Complexity

Yang

Nie

Jin

2021

Preprint

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In this paper, we study a delayed diffusive predator-prey model with nonlocal competition in prey and habitat complexity. The local stability of coexisting equilibrium are studied by analyzing the eigenvalue spectrum. Time delay inducing Hopf bifurcation is investigated by using time delay as bifurcation parameter. We give some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution by utilizing the normal form method and center manifold theorem. Our results suggest that only nonlocal competition and diffusion together can induce stably spatial inhomogeneous bifurcating periodic solutions.

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A delay-induced predator–prey model with Holling type functional response and habitat complexity

Cited by 38 publications

References 43 publications

Time-delay effect on a diffusive predator–prey model with habitat complexity

Time-delay effect on a diffusive predator–prey model with habitat complexity

Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping

Spatiotemporal Dynamics Induced by Nonlocal Competition in a Diffusion Predator-Prey System with Habitat Complexity

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