Global structure of the orbits of a kind of n-dimensional competitive systems

This paper discusses the global structure of the orbits of a kind of n-dimensional competitve systems, under the conditions that the equilibrium O is not weakly repulsive, we have established results which are similar to that obtained by Hirsch but are extended to a more generalized system. Also, the result of Yuan (which holds for n = 3) is generalized to the case of n > 3 and the result of Bendixson is generalized from a plane to one of dimension n. We then apply the result to a model of a negative feedback cellular control process and obtain that when n = 3, the unique periodic orbit of the model is stable. Copyright © 1995 Fuzhou University.