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An ecogenetic model with Michaelis-Menten functional response

Md. Sabiar Rahman

Abstract



The present investigation deals with an eco-genetic model introducing Michaelis-Menten (ratio-dependent) functional response of two genetically distinguished prey population having influence of predator population on its evolution. A detailed mathematical analysis of the up-dated system are systematically described and find out the conditions for which no trajectory can reach the origin following any fixed direction or spirally. The predator-free sub system can be destabilized by the predators under a suitable parametric restriction. The model system reveals that the solution coexists at a stable steady state. Also conditions of non-existence of periodic solutions around coexistence equilibrium with the successful application of the Bendixson‘s criterion has been executed. Finally, a conclusion of the ecological implications of the analytical and numerical findings are discussed as well.

Keywords


An eco-genetic model; Ratio Dependent; Persistence; Global Stability ; Bifurca-tion; Ecological implications.

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