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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 $dx/dt=rx\left( 1-{x\over k}\right) -{yx\over a+x},\qquad dy/dt=y \left(-d+{x \over a+x}\right)-h,\tag{*}$ 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.
For the entire collection see [Zbl 0903.00038].

##### MSC:
 34C23 Bifurcation theory for ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 37G99 Local and nonlocal bifurcation theory for dynamical systems
##### Keywords:
bifurcation; Bogdanov-Takens singularity