Global asymptotic behavior of a two-dimensional difference equation modelling competition
Date of Original Version
We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = xn/a + cyn, yn+1 = yn/b + dxn, n = 0,1, ..., where the parameters a and b are in (0,1), c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior. In the case where a = b we find an explicit equation for the stable manifold. © 2003 Elsevier Science Ltd. All rights reserved.
Nonlinear Analysis, Theory, Methods and Applications
Clark, Dean, M. R. Kulenović, and James F. Selgrade. "Global asymptotic behavior of a two-dimensional difference equation modelling competition." Nonlinear Analysis, Theory, Methods and Applications 52, 7 (2003): 1765-1776. doi:10.1016/S0362-546X(02)00294-8.