Speaker
Description
This work investigates the three species of one-predator-two-prey ecological models in Lotka-Volterra type functional response with or without diffusive terms.
Without the diffusive effects and under two essential assumptions, we generically classify all global dynamics completely. The global asymptotically stabilities of three equilibria are shown analytically in each case. Alternatively, with the diffusive term, we establish the existence of traveling wave solutions by the higher dimensional shooting method, the Wazewski principle. In particular, there are two critical wave speeds $0<c_2<c_1$. We show the existence of traveling wave solutions with the wave speed $c$ if $c>c_1$ and the non-existence of traveling wave solutions if $0<c<c_2$. Finally, a brief discussion, biological interpretations, and numerical simulations are given.
