Existence of Coexistence States: A Generic Property for Cyclic 3-Dimensional Competitive Systems

In this paper we consider the class C T of all dissipative 3-dimensional T-periodic Kolmogorov competitive and cyclic systems such that the trivial solution is a source, and we prove that “almost” every such system possesses a coexistence state. More precisely, we characterize an open and dense subset U of C T , with respect to the topology of the uniform convergence in compact sets, such that each member of U has a coexistence state.