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 functional response.The analysis is carried out both analytically and numerically.We use dynamical toolbox MATCONT to perform numerical bifurcation analysis.Our bifurcation analysis Gift in a Tin of the model indicates that it exhibits numerous types of bifurcation phenomena, including fold, subcritical Hopf, cusp, Bogdanov-Takens.

By Wheels (Accessories) starting 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.