Numerical bifurcation and stability analysis of an predator-prey system with generalized Holling type III functional response

Numerical bifurcation and stability analysis of an predator-prey system with generalized Holling type III functional response

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We perform a bifurcation analysis of a predator-prey model with Holling animed aniflex complete functional response.The analysis is carried out both analytically and numerically.We use dynamical toolbox MATCONT to perform numerical bifurcation analysis.

Our bifurcation analysis of the model indicates that it exhibits numerous types of bifurcation phenomena, including fold, subcritical Hopf, cusp, Bogdanov-Takens.By starting galaxy harmony nc from a Hopf bifurcation point, we approximate limit cycles which are obtained, step by step, using numerical continuation method and compute orbitally asymptotically stable periodic orbits.