On the Neimark-Sacker bifurcation in a discrete predator-prey model

Andrew Hone (University of Kent)

Thursday 10th November, 2011 14:00-15:00 Maths-Stats Bldg, LT 325

Abstract

The Hopf bifurcation, leading to the appearance of a limit cycle, is a well known phenomenon in the theory of differential equations, which arises in many different models. In this talk, we discuss its discrete analogue, namely the Neimark-Sacker bifurcation which appears in the context of difference equations. As our main example, we consider a discrete model for a predator-prey interaction, which generalizes a model considered by Murray. The relevance of this bifurcation and the differences between the discrete and continuous case will also be briefly discussed.

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