Spreading speeds for one species invading the habitat of two competitors in reaction-diffusion systems

This article is concerned with the spreading speeds of three-equation reaction-diffusion systems. From the perspective of population dynamics, we model the invasion of a new species into the shared habitat of two competitors, in which all three species eventually achieve a coexistence state. Notably, except for one case, all other versions of the system are not essentially order-preserving. When the initial value of the invader decays rapidly, we establish sufficient conditions for the spreading speed determined linearly. When the initial value exhibits different decay behaviors, the spreading speeds are explicitly derived. Moreover, we show the final convergence to the coexistence state.