Global asymptotic behavior of a two-dimensional system of difference equations modeling cooperation
Date of Original Version
We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = Axn yn/1+yn, y+1 = Byn xn/1+xn, n = 0,1,... where the parameters A and B are in (0, ∞) 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 the basins of attraction of two types of asymptotic behavior.
Journal of Difference Equations and Applications
Kulenović, M. R.S., and M. Nurkanović. "Global asymptotic behavior of a two-dimensional system of difference equations modeling cooperation." Journal of Difference Equations and Applications 9, 1 (2003): 149-159. doi:10.1080/1023619031000060981.