Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge

@article{Guan2011SpatiotemporalDO,
  title={Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge},
  author={Xiaona Guan and Weiming Wang and Yongli Cai},
  journal={Nonlinear Analysis-real World Applications},
  year={2011},
  volume={12},
  pages={2385-2395}
}
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 prey refuge. We establish a Lyapunov function to prove the global stability of the equilibria with diffusion and determine the Turing space in the spatial domain. Furthermore, we perform a series of numerical simulations and find that the model dynamics exhibits complex Turing pattern replication: stripes… Expand
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References

SHOWING 1-10 OF 43 REFERENCES
Spatiotemporal complexity of a ratio-dependent predator-prey system.
TLDR
The study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves, which may help to better understand the dynamics of an aquatic community in a real marine environment. Expand
Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters
Abstract A modified Leslie–Gower-type prey–predator model composed of a logistic prey with Holling’s type II functional response is studied. The axial point (1, 0) is found to be globallyExpand
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
Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability
Abstract In this work, we use an analytical approach to study the dynamic consequences of the simplest forms of refuge use by the prey. Although this problem is not new, there are surprisingly fewExpand
Three Limit Cycles in a Leslie--Gower Predator-Prey Model with Additive Allee Effect
TLDR
This work analyzes a bidimensional continuous-time differential equations system derived of Leslie-type predator-prey schemes by considering a nonmonotonic functional response and Allee effect on population prey, and shows that, under certain conditions over the parameters, the system allows the existence of three limit cycles. Expand
Analysis of a Model Predator-Prey System with Refuges
Abstract We study a model of a predator-prey system with refuges proposed in McNair [Theoret. Population Biol.29 (1986), 38-63]. We show that all solutions are ultimately bounded and eventually enterExpand
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
Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge.
TLDR
The most significant result of this analysis is the existence of a temperature interval in which increasing the amount of refuge dynamically destabilizes the system; and on part of this interval the interaction is less likely to persist in that predator and prey minimum population densities are lower than when no refuge is available. Expand
RETRACTED: Bifurcation analysis in the delayed Leslie–Gower predator–prey system
In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses someExpand
On a Leslie―Gower predator―prey model incorporating a prey refuge
Abstract We propose a Leslie–Gower predator–prey model incorporating a prey refuge. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system isExpand
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