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Displaying similar documents to “Periodic solutions of a three-species food chain model.”

Dynamics in a discrete predator-prey system with infected prey

Changjin Xu, Peiluan Li (2014)

Mathematica Bohemica

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In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...