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Global behavior of two competitive rational systems of difference equations in the plane. (English) Zbl 1180.37053
Summary: We investigate the global dynamics of solutions of two distinct competitive rational systems of difference equations in the plane. We show that the basins of attraction of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or of non-hyperbolic equilibrium points. Our results give complete answer to Open Problem 1 posed recently in [E. Camouzis, M. R. S. Kulenović, G. Ladas and O. Merino, J. Difference Equ. Appl. 15, No. 3, 303–323 (2009; Zbl 1169.39010)].
MSC:
37E30Homeomorphisms and diffeomorphisms of planes and surfaces
37G99Local and nonlocal bifurcation theory
39A10Additive difference equations