Global behaviour of n-dimensional Lotka-Volterra systems
Abstract
In this paper we study the behaviour of Lotka-Volterra systems; the principal tools are results from positivity and auxiliary functions that decrease along the trajectories; one typical result is that, if a decomposition of the interaction matrix into a product of a symmetric and an off-diagonal nonnegative matrix is possible, then all the trajectories either go to equilibria or cannot remain in any compact set of the interior of the positive orthant.