A Genralist Predator Prey Mathematical Model Analysis on a Cusp Point and Bogdanov-Takens Bifurcation Point

Temesgen Tibebu Mekonnen

International Journal of Mathematical Research, 2015, vol. 4, issue 2, 64-75

Abstract: This study considers a generalist predator-prey system. We investigate a local bifurcation namely Bogdanov-Takens (co dimension 2) bifurcations and a cusp point on two significant points in the division of parameter space. These points show the place where Bogdanov-Takens point and a cusp point exist. The existence of these bifurcations proved analytically by Normal form derivation. To reach the analysis we first studied the steady state solutions and their dependence on parameters and then investigate a parameter space which is divided into subregions based on the number of equilibrium points. We identified three vital parameters

Keywords: Couple differential equations; Parameter space; Cusp point; Bogdanov-takens bifurcation point; Normal form derivation (search for similar items in EconPapers)
Date: 2015
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