Bifurcation analysis in a predator–prey system with a functional response increasing in both predator and prey densities
Nonlinear Dynamics(2018)
摘要
This paper presents a qualitative study of a predator–prey interaction system with the functional response proposed by Cosner et al. (Theor Popul Biol 56:65–75, 1999 ). The response describes a behavioral mechanism which a group of predators foraging in linear formation searches, contacts and then hunts a school of prey. On account of the response, strong Allee effects are induced in predators. In the system, we determine the existence of all feasible nonnegative equilibria; further, we investigate the stabilities and types of the equilibria. We observe the bistability and paradoxical phenomena induced by the behavior of a parameter. Moreover, we mathematically prove that the saddle-node, Hopf and Bogdanov–Takens types of bifurcations can take place at some positive equilibrium. We also provide numerical simulations to support the obtained results.
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关键词
Predator–prey, Bistability, Allee effect, Saddle-node, Bogdanov–Takens, Hopf bifurcation, 34C23, 92D25
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