Existence of trajectories joining critical points for a symbiotic system via the Conley index
A sufficient condition for the existence of trajectories joining critical points of ecological system with three species is derived. Under some special geometric conditions concerning the behaviour of the vector field, the result follows by constructing suitable index pairs and the application of the Conley index theory. The result is very similar to the previous one, published by the author and \textit{X.-X. Wang} [The existence and uniqueness of trajectories joining critical points for differential equations in \(\mathbb{R}^3\), Chaos Solitons Fractals 12, No. 1, 153-158 (2001)].
scientific article; zbMATH DE number 1781535