| Abstract: |
| In this talk, we study a reaction-diffusion model for two competing biological species ($u$ and $v$) with Allee effects. Under one-side or two-side Allee effect, the model demonstrates complexity on its coexistence steady states. The conditions for persistence and competitive exclusion of the species are obtained through asymptotic stability with attraction regions and convergent rates depending on the biological parameters. Using the upper-lower solution method, we further prove that for a family of wave speeds, there exist traveling wave solutions connecting various steady-state solutions. Finally, numerical simulations are also presented to illustrate the theoretical results and population dynamics. |
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