| Abstract: |
| We analyze a differential equation model for the population dynamics of multiple species in a competitive environment. The model incorporates key ecological factors, including the conversion of available resources into per capita growth, the intrinsic harvest rate per unit area, and a uniform mortality rate. These factors influence interspecies competition and survival strategies, leading to the emergence and stability of three types of equilibrium states: extinction, competitive exclusion, and coexistence. Additionally, through a quasilinear reaction-diffusion system that models habitat selection strategies and ideal directed movement, we investigate the pattern of populations approaching coexistence equilibrium through traveling wave solutions. |
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