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Zbl 1205.34058
Wang, Xiaoli; Du, Zengji; Liang, Jing
Existence and global attractivity of positive periodic solution to a Lotka-Volterra model. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 5, 4054-4061 (2010). ISSN 1468-1218

Summary: By using Mawhin's continuation theorem and constructing a suitable Lyapunov functional, a Lotka-Volterra model with mutual interference and Holling III type functional response is studied. Some sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive periodic solution of the model. Furthermore, the conditions are related to the interference constant $m$.

MSC 2000:: *34C60 Applications of qualitative theory of ODE
34C05 Qualitative theory of some special solutions of ODE
92D25 Population dynamics
34D20 Lyapunov stability of ODE
47N20 Appl. of operator theory to differential and integral equations

Keywords: global attractivity; Mawhin's construction theorem; positive periodic solution; Lyapunov functional; Holling III type functional response

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