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Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting. (English) Zbl 0917.34029
Ruan, Shigui (ed.) et al., Differential equations with applications to biology. Proceedings of the international conference, Halifax, Canada, July 25–29, 1997. Providence, RI: American Mathematical Society. Fields Inst. Commun. 21, 493-506 (1999).

Consider the differential system

dx/dt=rx1-x k-yx a+x,dy/dt=y-d+x a+x-h,(*)

describing a predator-prey system with constant rate harvesting. k,d,r,a and h are positive parameters. The paper contains a bifurcation analysis of (*). The existence of a Bogdanov-Takens bifurcation is established under some conditions.

MSC:
34C23Bifurcation (ODE)
34C05Location of integral curves, singular points, limit cycles (ODE)
37G99Local and nonlocal bifurcation theory