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Global behavior of four competitive rational systems of difference equations in the plane. (English) Zbl 1177.37046

Summary: We investigate the global dynamics of solutions of four distinct competitive rational systems of difference equations in the plane. We show that the basins of attractions of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or nonhyperbolic equilibrium points. Our results give complete answer to Open Problem 2 posed recently by E. Camouzis et al. [J. Difference Equ. Appl. 15, No. 3, 303–323 (2009; Zbl 1169.39010)].

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37G99 Local and nonlocal bifurcation theory for dynamical systems
39A10 Additive difference equations

Citations:

Zbl 1169.39010
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References:

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