an:00599888
Zbl 0802.34064
Zhu, Hsiu-Rong; Smith, Hal L.
Stable periodic orbits for a class of three dimensional competitive systems
EN
J. Differ. Equations 110, No. 1, 143-156 (1994).
0022-0396
1994
j
34D20 34D30 37C75 92D25
dissipative, three-dimensional, competitive, and irreducible system of ordinary differential equations; orbitally stable periodic orbit
From the authors' abstract: ``It is shown that for a dissipative, three- dimensional, competitive, and irreducible system of ordinary differential equations having a unique equilibrium point, at which point the Jacobian matrix has negative determinant, either the equilibrium point is stable or there exists an orbitally stable periodic orbit. If in addition, the system is analytic then there exists an orbitally asymptotically stable periodic orbit when the equilibrium is unstable. The additional assumption of analyticity can be replaced by the assumption that the equilibrium point and every periodic orbit are hyperbolic. In this case, the Morse-Smale conditions hold and the flow is structurally stable''.
M.A.Teixeira (Campinas)