Summary
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.
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Rothe, F. Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. J. Math. Biol. 3, 319–324 (1976). https://doi.org/10.1007/BF00275064
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DOI: https://doi.org/10.1007/BF00275064