Limit cycles in two-dimensional predator-prey systems, Robert Kooij (Delft University of Technology, Netherlands)
:
Monday, 04. April 2022, 15:00
- Abstract: In this talk, we discuss two-dimensional predator-prey systems, in particular the generalized Gause model. This model assumes a logistic growth rate for the prey in the absence of the predator, and a constant death rate for the predator. Often it is assumed that the functional response, i.e. the capture rate of prey per predator, is an analytical function, such as the functional response of Holling Type II and III. The aim of this talk is to discuss the generalized Gause model for several classes of non-analytical functional responses. Our main interest is the number of closed orbits of the systems under consideration. We will show that the system with a non-analytical functional response shows richer dynamics than their analytical counterparts. As examples of this more complicated behavior, we mention: the co-existence of a stable equilibrium with a stable limit cycle and the co-existence of a family of closed orbits and a limit cycle.