Qualitative Analysis for Predator-Prey Systems with Time Delays and Simplified Holling Type-IV Functional Response

doi:https://doi.org/10.1115/1.859919.paper253

Qualitative Analysis for Predator-Prey Systems with Time Delays and Simplified Holling Type-IV Functional Response

Nannan Zhang,Jing Xu,Yongfeng Ma-2011-01-01-ASME Press eBooks

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TL;DRAbstract

In this paper,a predator-prey systems with time delays and simplified Holling type-IV functional response is investigated, the predator's numerical response has Leslie form.Proved that the solutions with positive initial values are positive and bounded. Give the existence conditions of the positive equilibrium point and prove the equilibrium point is uniqued. Given the conditions of local asymptotic stability by Routh-Hurwiitz theroy.The impact of the time delay on the stability of the model is considered by choosing the delay time 1 as a bifurcation parameter, the existence of Hopf bifurcation is also found by bifurcation theory.

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In this paper,a predator-prey systems with time delays and simplified Holling type-IV functional response is investigated, the predator's numerical response has Leslie form.Proved that the solutions with positive initial values are positive and bounded. Give the existence conditions of the positive equilibrium point and prove the equilibrium point is uniqued. Given the conditions of local asymptotic stability by Routh-Hurwiitz theroy.The impact of the time delay on the stability of the model is considered by choosing the delay time 1 as a bifurcation parameter, the existence of Hopf bifurcation is also found by bifurcation theory.

Keywords

Functional responseMathematicsHopf bifurcationEquilibrium pointBifurcationStability (learning theory)Applied mathematicsType (biology)

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