| Contents |
| In this talk, we first review some existing results on a combined mathematical model of resource and sexual competition. The population dynamics (competitive exclusion and coexistence) in this model is analyzed through a coupled system of reaction-diffusion equations. Through construction of smooth upper-lower solutions, the traveling wave solutions of this complex competition system are shown to exist for a family of wave speeds. When strong sexual competition and low growth rate lead to competitive exclusion of the biological species, we obtain the traveling wave solution connecting the corresponding equilibria. Models with sexual competition affecting one or both species are considered and compared. |
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