Global behavior of n-dimensional Lotka-Volterra systems.
The behavior of Lotka-Volterra systems is studied using as tools the 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.
Gouzé
J L
JL
INRIA, Sophia-Antipolis, Valbonne, France.
D000818:Animals; D006790:Host-Parasite Interactions; D008433:Mathematics; D008954:Models, Biological; D011235:Predatory Behavior; D013559:Symbiosis