title: Convergence to the equilibrium state in the Volterra-Lotka diffusion equations.
abstract: We introduce a diffusion term in the Volterra-Lotka model for two interacting species. For certain simple boundary conditions there exists a Lyapunov functional which allows to investigate the asymptotic behavior. Either the solution converges to equilibrium or sustained oscillations occur.
mesh_terms: D004058:Diffusion; D008954:Models, Biological; D010507:Periodicity; D011156:Population Density