Global stability of Leslie-type predator-prey model

Qi, Yingyong; Zhu, Yi

doi:10.4310/maa.2016.v23.n3.a3

Cited by 5 publications

(4 citation statements)

References 3 publications

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“…Indeed (1.6) holds when a is nearly constant or when b is sufficiently small (see Remark 2.6). We also remark that the global stability of the positive constant steady state of (1.1) is proved in [20,21] with weaker condition on b but constant a and…”

Section: Introductionmentioning

confidence: 88%

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Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

Ni¹,

Shi

Wang

2020

Preprint

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Section: Introductionmentioning

confidence: 88%

“…When r = 0 in (1.1), the system becomes to the Leslie-Gower predator-prey model. The global stability for that case including delay effect was investigated in [3,20] when a and d i are constants, see also [4,12,14,15] for related work.…”

Section: Introductionmentioning

confidence: 99%

Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

Ni¹,

Shi

Wang

2020

Preprint

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“…For this scenario, its unique interior equilibrium still is globally asymptotically stable under certain conditions. The PDE version of the Leslie-Gower model also has been studied extensively, see [7,17,24,29].…”

Section: Na Min and Mingxin Wangmentioning

confidence: 99%

Hopf bifurcation and steady-state bifurcation for a Leslie-Gower prey-predator model with strong Allee effect in prey

Min¹,

Wang²

2019

Discrete &Amp; Continuous Dynamical Systems - A

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It is well known that the Leslie-Gower prey-predator model (without Allee effect) has a unique globally asymptotically stable positive equilibrium point, thus there is no Hopf bifurcation branching from positive equilibrium point. In this paper we study the Leslie-Gower prey-predator model with strong Allee effect in prey, and perform a detailed Hopf bifurcation analysis to both the ODE and PDE models, and derive conditions for determining the steady-state bifurcation of PDE model. Moreover, by the center manifold theory and the normal form method, the direction and stability of Hopf bifurcation solutions are established. Finally, some numerical simulations are presented. Apparently, Allee effect changes the topology structure of the original Leslie-Gower model.

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“…where Ω is a bounded and smooth domain of R N . The global stability of a 1+b , a 1+b for the problem (P) had been studied by many authors, see [3,5,20] for example.…”

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confidence: 99%

Dynamics for the diffusive Leslie-Gower model with double free boundaries

Wang¹,

Zhang²

2018

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries represent expanding fronts of the predator species. We first prove the existence, uniqueness and regularity of global solution. Then provide a spreading-vanishing dichotomy, namely the predator species either successfully spreads to infinity as t → ∞ at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run. The long time behavior of (u, v) and criteria for spreading and vanishing are also obtained. Because the term v/u (which appears in the second equation) may be unbounded when u nears zero, it will bring some difficulties for our study.

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Global stability of Leslie-type predator-prey model

Cited by 5 publications

References 3 publications

Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

Hopf bifurcation and steady-state bifurcation for a Leslie-Gower prey-predator model with strong Allee effect in prey

Dynamics for the diffusive Leslie-Gower model with double free boundaries

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