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Existence and global attractivity of positive periodic solution to a Lotka-Volterra model. (English) Zbl 1205.34058
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 $m$.

34C60Qualitative investigation and simulation of models (ODE)
34C05Location of integral curves, singular points, limit cycles (ODE)
92D25Population dynamics (general)
34D20Stability of ODE
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
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