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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.
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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