The nondimensionalized Bazykin model with ratio-dependent functional response has up to two interior equilibria, with P1 a saddle and P2 stable or unstable, and undergoes saddle-node, Hopf, homoclinic, and Bogdanov-Takens bifurcations.
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Bifurcation analysis of a prey-predator model with predator intra-specific interactions and ratio-dependent functional response
The nondimensionalized Bazykin model with ratio-dependent functional response has up to two interior equilibria, with P1 a saddle and P2 stable or unstable, and undergoes saddle-node, Hopf, homoclinic, and Bogdanov-Takens bifurcations.