Stability and bifurcation analysis for a discrete‐time model of Lotka–Volterra type with delay

Stability and bifurcation analysis for a discrete‐time model of Lotka–Volterra type with delay

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Article ID: iaor20113276
Volume: 217
Issue: 12
Start Page Number: 5449
End Page Number: 5457
Publication Date: Feb 2011
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: stationary points, Volterra equations
Abstract:

A discrete model of Lotka–Volterra type with delay is considered, and a bifurcation analysis is undertaken for the model. We derive the precise conditions ensuring the asymptotic stability of the positive equilibrium, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, fold or Neimark–Sacker bifurcations occur, but codimension 2 (fold‐Neimark–Sacker, double Neimark–Sacker and resonance 1:1) bifurcations may also be present. The direction and the stability of the Neimark–Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory.

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