Prey switching with a linear preference trade-off

© 2014 Society for Industrial and Applied Mathematics. In ecology, prey switching refers to a predator's adaptive change of habitat or diet in response to prey abundance. In this paper, we study piecewise-smooth models of predator-prey interactions with a linear trade-off in a predator's prey preference. We consider optimally foraging predators and derive a model for a 1 predator-2 prey interaction with a tilted switching manifold between the two sides of discontinuous vector fields. We show that the 1 predator-2 prey system undergoes a novel adding-sliding-like (center to two-part periodic orbit; "C2PO") bifurcation in which the prey ratio transitions from constant to time-dependent. Farther away from the bifurcation point, the period of the oscillating prey ratio doubles, which suggests a possible cascade to chaos. We compare our model predictions with data on freshwater plankton, and we successfully capture the periodicity in the ratio between the predator's preferred and alternative prey types. Our study suggests that it is useful to investigate prey ratio as a possible indicator of how population dynamics can be influenced by ecosystem diversity.