Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5

predator-prey model Related Publications

5 Uniformly Strong Persistence for a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes

Authors: Changjin Xu, Yusen Wu

Abstract:

In this paper, a asymptotically periodic predator-prey model with Modified Leslie-Gower and Holling-Type II schemes is investigated. Some sufficient conditions for the uniformly strong persistence of the system are established. Our result is an important complementarity to the earlier results.

Keywords: predator-prey model, uniformly strong persistence, asymptotically periodic, Holling-type II

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4 Permanence and Global Attractivity of a Delayed Predator-Prey Model with Mutual Interference

Authors: Kai Wang, Yanling Zu

Abstract:

By utilizing the comparison theorem and Lyapunov second method, some sufficient conditions for the permanence and global attractivity of positive periodic solution for a predator-prey model with mutual interference m ∈ (0, 1) and delays τi are obtained. It is the first time that such a model is considered with delays. The significant is that the results presented are related to the delays and the mutual interference constant m. Several examples are illustrated to verify the feasibility of the results by simulation in the last part.

Keywords: delays, predator-prey model, mutual interference, permanence, Global attractivity

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3 Positive Periodic Solutions for a Predator-prey Model with Modified Leslie-Gower Holling-type II Schemes and a Deviating Argument

Authors: Kai Wang, Yanling Zhu

Abstract:

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

Keywords: predator-prey model, Holling II type functional response, positive periodic solution, coincidence degree theorem

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2 Bifurcation Analysis of a Delayed Predator-prey Fishery Model with Prey Reserve in Frequency Domain

Authors: Changjin Xu

Abstract:

In this paper, applying frequency domain approach, a delayed predator-prey fishery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

Keywords: Stability, Hopf Bifurcation, frequency domain, predator-prey model, Nyquist criterion

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1 Uniformly Persistence of a Predator-Prey Model with Holling III Type Functional Response

Authors: Yanling Zhu

Abstract:

In this paper, a predator-prey model with Holling III type functional response is studied. It is interesting that the system is always uniformly persistent, which yields the existence of at least one positive periodic solutions for the corresponding periodic system. The result improves the corresponding ones in [11]. Moreover, an example is illustrated to verify the results by simulation.

Keywords: predator-prey model, Uniformly persistence, Comparisontheorem, Holling III type functional response

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