Title

Global bifurcation for discrete competitive systems in the plane

Document Type

Article

Date of Original Version

7-1-2009

Abstract

A global bifurcation result is obtained for families of competitive systems of difference equations {xn+l = fa(Xn,yn) yn+1 = 9α(Xn,yn) where α is a parameter, fα and gα are continuous real valued functions on a rectangular domain Rα C R2 such that fα(x, y) is non-decreasing in x and non-increasing in y, and gα(x,y) is non-increasing in x and non-decreasing in y. A unique interior fixed point is assumed for all values of the parameter α. As an application of the main result for competitive systems a global period-doubling bifurcation result is obtained for families of second order difference equations of the type x n+l=Fα(xn-l), n = 0,1,... where α is a parameter, Iα is a decreasing function in the first variable and increasing in the second variable, and Iα is a interval in R, and there is a unique interior equilibrium point. Examples of application of the main results are also given.

Publication Title

Discrete and Continuous Dynamical Systems - Series B

Volume

12

Issue

1

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