The Mathematical Institute, University of Oxford, Eprints Archive

Prey switching with a linear preference trade-off

Piltz, S and Porter, M A and Maini, P. K. (2014) Prey switching with a linear preference trade-off. SIAM Journal on Applied Mathematics, 13 (2). pp. 658-682. ISSN 1095-712X

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Lotka--Volterra interaction, Filippov systems, adding-sliding bifurcation, planktonic protozoa-algae dynamics
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1836
Deposited By: Philip Maini
Deposited On:25 Apr 2014 07:48
Last Modified:29 May 2015 19:31

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