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Global behavior of a class of three-dimensional competitive systems. (English) Zbl 0838.34060
The 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.
##### 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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