For the strongly competitive Lotka-Volterra system in R^N, the spreading speed of the winning species is the scalar Fisher-KPP speed in one regime and the bistable front speed in another, with a direction-dependent variational formula for separated initial data.
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Asymptotic speeds of spreading for the Lotka-Volterra system with strong competition in $\mathbb{R}^N$
For the strongly competitive Lotka-Volterra system in R^N, the spreading speed of the winning species is the scalar Fisher-KPP speed in one regime and the bistable front speed in another, with a direction-dependent variational formula for separated initial data.