Modified Leslie-Gower Functional Response Research Articles

Global boundedness and dynamics of a diffusive predator–prey model with modified Leslie–Gower functional response and density-dependent motion

This paper is devoted to studying the dynamical behaviors and stationary patterns of a diffusive modified Leslie–Gower predator–prey model with density-dependent motion in the predator population. We establish the existence of classical solutions with the uniform-in time bound and then analyze the local and global stability of the spatially homogeneous co-existence steady state under certain parametric conditions. By choosing the prey diffusion rate d2 as the bifurcation parameter, the steady state bifurcations from the positive constant equilibrium solution are investigated. Numerical simulations are performed to corroborate our analytical findings.

An Impulsive Predator–Prey System with Modified Leslie–Gower Functional Response and Diffusion

An Impulsive Predator–Prey System with Modified Leslie–Gower Functional Response and Diffusion

Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge

Abstract In this paper, we consider the optimal harvesting controls for a diffusive predator-prey system, which is formulated by prey refuge and modified Leslie-Gower functional response. The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition. The nonexistence and existence of nonconstant steady states are obtained by Leray-Schauder degree theory. Also, the optimal harvesting strategies to get maximum sustainable yield (MSY) and maximum economic yield (MEY) are correspondingly given.

The Effect of Delay on A Diffusive Predator–Prey System with Modified Leslie–Gower Functional Response

In this paper, a delayed diffusive modified Leslie–Gower-type predator–prey model with Beddington–DeAngelis functional response subject to Neumann boundary condition is considered. The stability/instability of the non-negative equilibria and a detailed Hopf bifurcation analysis are investigated. And explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of normal form and center manifold. In addition, some numerical simulations are carried out.

Instability and Pattern Formation in Three-Species Food Chain Model via Holling Type II Functional Response on a Circular Domain

This paper is devoted to the study of food chain predator–prey model. This model is given by a reaction–diffusion system defined on a circular spatial domain, which includes three-state variables namely, prey and intermediate predator and top predator and incorporates the Holling type II and a modified Leslie–Gower functional response. The aim of this paper is to investigate theoretically and numerically the asymptotic behavior of the interior equilibrium of the model. The local and global stabilities of the positive steady-state solution and the conditions that enable the occurrence of Hopf bifurcation and Turing instability in the circular spatial domain are proved. In the end, we carry out numerical simulations to illustrate how biological processes can affect spatiotemporal pattern formation in a disc spatial domain and different types of spatial patterns with respect to different time steps and diffusion coefficients are obtained.

Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain

In this paper, we investigate theoretically and numerically a 2-D spatio-temporal dynamics of a predator-prey mathematical model which incorporates the Holling type II and a modified Leslie–Gower functional response and logistic growth of the prey. This system is modeled by a reaction diffusion equations defined on a disc domain {(x,y)∈R2/x2+y2<R2} with Dirichlet initial conditions and Neumann boundary conditions. We study the local and global stability of the positive equilibrium point. We show that the diffusion can induce instability of the uniform equilibrium point which is stable with respect to a constant perturbation as shown by Turing in 1950s and derive the conditions for Hopf and Turing bifurcation in the spatial domain. Numerical results are given in order to illustrate how biological processes affect spatiotemporal pattern formation in a spatial domain. We perform the computations and generalize, on a circular domain, the results presented in Camara and Aziz-Alaoui [6].

Global asymptotical stability and persistent property for a diffusive predator–prey system with modified Leslie–Gower functional response

A diffusive predator–prey system with modified Holling–Tanner functional response and no-flux boundary condition is considered in this work. A sufficient condition which ensures persistence of the system is obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using a comparison method. It is shown that our result supplements and complements one of the main results of Shi et al. [H.B. Shi, W.T. Li, G. Lin, Positive steady states of a diffusive predator–prey system with modified Holling–Tanner functional response, Nonlinear Analysis: Real World Applications 11 (2010) 3711–3721].

Complexity in a prey-predator model

In this paper we consider a predator-prey model given by a reaction-diffusion system. It incorporates the Holling-type-II and a modified Leslie-Gower functional response. We focus on qualitaive analysis, bifurcation mecanisms and patterns formation. Nous considérons un modèle proie-prédateur exprimé sous forme de système de réaction diffusion. En absence de diffusion, le système étudié est de type Holling-type-II et la réponse fonctionnelle une forme modifiée du terme de Leslie-Gower. Dans cet article, nous nous intéressons à l’analyse qualitative des solutions , l’étude des bifurcations et la formation de motifs spatio-temporels.