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, e.g., Journal
Discrete and Continuous Dynamical Systems - Series B
Volume
12
Issue
1
Citation/Publisher Attribution
Kulenović, M. R., and Orlando Merino. "Global bifurcation for discrete competitive systems in the plane." Discrete and Continuous Dynamical Systems - Series B 12, 1 (2009): 133-149. doi: 10.3934/dcdsb.2009.12.133.