Allee Effect - Explore the Science & Experts | ideXlab

Scan Science and Technology

Contact Leading Edge Experts & Companies

Allee Effect

The Experts below are selected from a list of 5694 Experts worldwide ranked by ideXlab platform

Allee Effect – Free Register to Access Experts & Abstracts

Weiming Wang – One of the best experts on this subject based on the ideXlab platform.

  • dynamics of a leslie gower predator prey model with additive Allee Effect
    Applied Mathematical Modelling, 2015
    Co-Authors: Weiming Wang, Yongli Cai, Caidi Zhao, Jinfeng Wang

    Abstract:

    Abstract In this paper, we investigate the complex dynamics of a Leslie–Gower predation model with additive Allee Effect on prey. Without Allee Effect, the model has a unique globally asymptotically stable equilibrium point under some conditions. With Allee Effect on prey, the model has none, one or two positive equilibria. Moreover, we prove the existence of parameter subsets for which the model can have Hopf bifurcation. And we find that when the model exhibits two positive equilibria there is a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. One of the most interesting findings is that Allee Effect can increase the risk of ecological extinction.

  • Dynamics of a Leslie–Gower predator–prey model with additive Allee Effect
    Applied Mathematical Modelling, 2015
    Co-Authors: Yongli Cai, Weiming Wang, Caidi Zhao, Jinfeng Wang

    Abstract:

    Abstract In this paper, we investigate the complex dynamics of a Leslie–Gower predation model with additive Allee Effect on prey. Without Allee Effect, the model has a unique globally asymptotically stable equilibrium point under some conditions. With Allee Effect on prey, the model has none, one or two positive equilibria. Moreover, we prove the existence of parameter subsets for which the model can have Hopf bifurcation. And we find that when the model exhibits two positive equilibria there is a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. One of the most interesting findings is that Allee Effect can increase the risk of ecological extinction.

  • dynamical complexity induced by Allee Effect in a predator prey model
    Nonlinear Analysis-real World Applications, 2014
    Co-Authors: Weiming Wang, Yanuo Zhu, Yongli Cai, Wenjuan Wang

    Abstract:

    Abstract In this paper, we investigate the complex dynamics induced by Allee Effect in a predator–prey model. For the non-spatial model, Allee Effect remains the boundedness of positive solutions, and it also induces the model to exhibit one or two positive equilibria. Especially, in the case with strong Allee Effect, the model is bistable. For the spatial model, without Allee Effect, there is the nonexistence of diffusion-driven instability. And in the case with Allee Effect, the positive equilibrium can be unstable under certain conditions. This instability is induced by Allee Effect and diffusion together. Furthermore, via numerical simulations, the model dynamics exhibits both Allee Effect and diffusion controlled pattern formation growth to holes, stripe–hole mixtures, stripes, stripe–spot mixtures, and spots replication. That is to say, the dynamics of the model with Allee Effect is not simple, but rich and complex.

Yongli Cai – One of the best experts on this subject based on the ideXlab platform.

  • dynamics of a leslie gower predator prey model with additive Allee Effect
    Applied Mathematical Modelling, 2015
    Co-Authors: Weiming Wang, Yongli Cai, Caidi Zhao, Jinfeng Wang

    Abstract:

    Abstract In this paper, we investigate the complex dynamics of a Leslie–Gower predation model with additive Allee Effect on prey. Without Allee Effect, the model has a unique globally asymptotically stable equilibrium point under some conditions. With Allee Effect on prey, the model has none, one or two positive equilibria. Moreover, we prove the existence of parameter subsets for which the model can have Hopf bifurcation. And we find that when the model exhibits two positive equilibria there is a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. One of the most interesting findings is that Allee Effect can increase the risk of ecological extinction.

  • Dynamics of a Leslie–Gower predator–prey model with additive Allee Effect
    Applied Mathematical Modelling, 2015
    Co-Authors: Yongli Cai, Weiming Wang, Caidi Zhao, Jinfeng Wang

    Abstract:

    Abstract In this paper, we investigate the complex dynamics of a Leslie–Gower predation model with additive Allee Effect on prey. Without Allee Effect, the model has a unique globally asymptotically stable equilibrium point under some conditions. With Allee Effect on prey, the model has none, one or two positive equilibria. Moreover, we prove the existence of parameter subsets for which the model can have Hopf bifurcation. And we find that when the model exhibits two positive equilibria there is a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. One of the most interesting findings is that Allee Effect can increase the risk of ecological extinction.

  • dynamical complexity induced by Allee Effect in a predator prey model
    Nonlinear Analysis-real World Applications, 2014
    Co-Authors: Weiming Wang, Yanuo Zhu, Yongli Cai, Wenjuan Wang

    Abstract:

    Abstract In this paper, we investigate the complex dynamics induced by Allee Effect in a predator–prey model. For the non-spatial model, Allee Effect remains the boundedness of positive solutions, and it also induces the model to exhibit one or two positive equilibria. Especially, in the case with strong Allee Effect, the model is bistable. For the spatial model, without Allee Effect, there is the nonexistence of diffusion-driven instability. And in the case with Allee Effect, the positive equilibrium can be unstable under certain conditions. This instability is induced by Allee Effect and diffusion together. Furthermore, via numerical simulations, the model dynamics exhibits both Allee Effect and diffusion controlled pattern formation growth to holes, stripe–hole mixtures, stripes, stripe–spot mixtures, and spots replication. That is to say, the dynamics of the model with Allee Effect is not simple, but rich and complex.

Chang-zhong Liu – One of the best experts on this subject based on the ideXlab platform.

  • analysis of a discrete time predator prey system with Allee Effect
    Ecological Complexity, 2011
    Co-Authors: Wan-xiong Wang, Yan-bo Zhang, Chang-zhong Liu

    Abstract:

    Abstract This paper deals with a discrete-time predator–prey system with Allee Effect. We obtain asymptotically stable conditions of the equilibrium points which are subject to the Allee Effect. The stabilizing Effect of Allee Effect on prey and predator populations is studied, respectively. The Allee Effect which occurs on both of predator and prey populations is also discussed by stability analysis, phase-plane and bifurcation diagram analysis. Our study suggests that Allee Effect has stabilizing Effect on population dynamics.

  • Analysis of a discrete-time predator–prey system with Allee Effect
    Ecological Complexity, 2011
    Co-Authors: Wan-xiong Wang, Yan-bo Zhang, Chang-zhong Liu

    Abstract:

    Abstract This paper deals with a discrete-time predator–prey system with Allee Effect. We obtain asymptotically stable conditions of the equilibrium points which are subject to the Allee Effect. The stabilizing Effect of Allee Effect on prey and predator populations is studied, respectively. The Allee Effect which occurs on both of predator and prey populations is also discussed by stability analysis, phase-plane and bifurcation diagram analysis. Our study suggests that Allee Effect has stabilizing Effect on population dynamics.