Traveling Wave Solutions of Lotka-Volterra Type Two Predators-One Prey diffusive models
楊定揮 副教授淡江數學系 下午 2:30–4:00 鴻經館 107 室Abstract :
In this work, we consider a three species diffusive food web model with one basal resource and two predators feeding by the same resource. It is well known that these two predators cannot coexist due to the Competitive Exclusion Principle. However, there are three non-trivial boundary equilibria. One the the saturated state of the prey without any predator $E_K$. Another two equilibria, $E_1$ and $E_2$, are the coexistence of the prey and one predator, respectively.
With a generic assumption, $E_2$ is globally asymptotically stable in the corresponding kinetic equation. Biologically, the assumption means one predator is superior in the resource exploitation. By a high dimensional shooting method, the Wazewski' principle, we show the existence of traveling wave solutions from $E_K$ to $E_2$ and $E_1$ to $E_2$. Finally, some numerical simulations are presented and some biological interpretations are given.