Bifurcations and Pattern Formation in a Predator-Prey Model

@article{Cai2018BifurcationsAP,
  title={Bifurcations and Pattern Formation in a Predator-Prey Model},
  author={Yongli Cai and Zhanji Gui and Xuebing Zhang and Hongbo Shi and Weiming Wang},
  journal={Int. J. Bifurc. Chaos},
  year={2018},
  volume={28},
  pages={1850140:1-1850140:17}
}
In this paper, we investigate the spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge subject to the Neumann boundary conditions. We mainly consider Hopf bifur... 
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References

SHOWING 1-10 OF 34 REFERENCES
Bifurcation and spatio-temporal patterns in a diffusive predator–prey system
Abstract A diffusive predator–prey system with predator functional response subject to Neumann boundary conditions is considered. Existence, nonexistence, and boundedness of non-constant positiveExpand
A Lyapunov function for Leslie-Gower predator-prey models
A Lyapunov function for continuous time Leslie-Gower predator-prey models is introduced. Global stability of the unique coexisting equilibrium state is thereby established.
Analysis of a predator–prey model with modified Leslie–Gower and Holling-type II schemes with time delay
Abstract Two-dimensional delayed continuous time dynamical system modeling a predator–prey food chain, and based on a modified version of Holling type-II scheme is investigated. By constructing aExpand
Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩
Abstract A diffusive predator–prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis areExpand
Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge.
TLDR
A diffusive predator-prey model with Holling type II functional response and the no-flux boundary condition incorporating a constant prey refuge and an algorithm for determining the properties of the Hopf bifurcation is derived. Expand
Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge
We study a predator–prey model with Holling type II functional response incorporating a prey refuge under homogeneous Neumann boundary condition. We show the existence and non-existence ofExpand
Dynamics and patterns of a diffusive Leslie–Gower prey–predator model with strong Allee effect in prey
Abstract This paper is devoted to study the dynamical properties and stationary patterns of a diffusive Leslie–Gower prey–predator model with strong Allee effect in the prey population. We firstExpand
Bifurcation Analysis of a Generic Reaction-Diffusion Turing Model
A generic Turing type reaction–diffusion system derived from the Taylor expansion near a constant equilibrium is analyzed. The existence of Hopf bifurcations and steady state bifurcations isExpand
Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect
Abstract In this work, a bidimensional continuous-time differential equations system is analyzed which is derived from Leslie type predator–prey schemes by considering a nonmonotonic functionalExpand
Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge
Abstract In this paper, we investigate the spatiotemporal dynamics of a two-dimensional predator–prey model, which is based on a modified version of the Leslie–Gower scheme incorporating a preyExpand
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