| Popis: |
In this work, we study a model of the interaction of N species (N > 2) which involves cross-diffusion. The model generalizes the model introduced in 1979 by Shigesada, Kawasaki and Teramoto for two species (SKT). All species are assumed to exhibit a functional response of the same form similar to SKT model. By constructing a Lyapunov functional of the system, we establish the global stability of the equilibrium, subject to some conditions on the cross-diffusion matrix and the diffusion vector. A sufficient condition is also derived for the coexistence of a large number of interacting species. Particular cases of the model for two species are considered extensively in the literature. Most of these results are shown to follow as consequences of the general theory developed here. |
