Limit cycles in a Gause-type predator-prey model with sigmoid functional response and weak Allee effect on prey

作者：Gonzalez Olivares Eduardo^*; Rojas Palma Alejandro

来源：Mathematical Methods in the Applied Sciences, 2012, 35(8): 963-975.

DOI：10.1002/mma.2509

• Allee effect
• sigmoid functional response
• predator-prey models
• limit cycle
• bifurcation

The goal of this work is to examine the global behavior of a Gause-type predatorprey model in which two aspects have been taken into account: (i) the functional response is Holling type III; and (ii) the prey growth is affected by a weak Allee effect. Here, it is proved that the origin of the system is a saddle point and the existence of two limit cycles surround a stable positive equilibrium point: the innermost unstable and the outermost stable, just like with the strong Allee effect. Then, for determined parameter constraints, the trajectories can have different????-?limit sets. The coexistence of a stable limit cycle and a stable positive equilibrium point is an important fact for ecologists to be aware of the kind of bistability shown here. So, these models are undoubtedly rather sensitive to disturbances and require careful management in applied contexts of conservation and fisheries.

• 出版日期2012-5-30