Global behavior of a class of three-dimensional competitive systems.

*(English)*Zbl 0838.34060The authors consider the three-dimensional competitive system (1) \(\dot X= F(X)\), \(F\in C^2: R^3\to R^3\), where \(X= (x_1, x_2, x_3)\), \(F= (f_1, f_2, f_3)\), \(\partial f_i(x)/\partial x_j\leq 0\), \(i\neq j\). The existence of invariant surfaces and the existence of semi-stable periodic orbits of the system (1) is proved.

Reviewer: Chen Lan Sun (Beijing)

##### MSC:

34D05 | Asymptotic properties of solutions to ordinary differential equations |

92D25 | Population dynamics (general) |

34C25 | Periodic solutions to ordinary differential equations |

34C30 | Manifolds of solutions of ODE (MSC2000) |

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\textit{J. Ruan}, Acta Math. Sin., New Ser. 11, No. 3, 316--323 (1995; Zbl 0838.34060)

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##### References:

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