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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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\textit{M. Garić-Demirović} et al., Discrete Dyn. Nat. Soc. 2009, Article ID 153058, 34 p. (2009; Zbl 1177.37046)

### References:

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