A Lyapunov Functional for a Predator-Prey Model with Nonlinear Predation Rate and Periodic Solutions

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Fatemion Aghda, Ashraf Alsadat | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42088 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaraki, Mahmoud
Abstract:
In this thesis we consider the dynamics of a general predator-prey model which generalizes several known predator-prey, assuming that the intrinsic growth rate of the pray, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for the stability of the equilibria. also, we consider a delayed periodic predator- prey model and sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solutions of the model.
Keywords:
Predator-Prey Model ; Lyapunov Function ; Periodic Solution ; Stability ; Equilibria Point

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