| Abstract: |
| We investigate reaction-diffusion models for two competing species exploiting a common standing resource. The dynamics are governed by a system of nonlinear differential equations admitting three equilibrium classes: extinction, competitive exclusion, and coexistence. Analytical conditions on the biological parameters ensuring the presence and asymptotic stability of these equilibria are derived, with particular emphasis on the coexistence equilibrium. When the level of available resources $R$ remains constant over an unbounded spatial domain, we further examine the global stability of the coexistence equilibrium via traveling wavefronts. Using the upper-lower solution method, we establish the existence of traveling wave solutions connecting the extinction or single-dominance states to the coexistence state for a continuum of wave speeds exceeding a biologically determined minimal value. If the level of available resources $R$ varies in space or time but remains bounded, the obtained results may be extended to provide insights into the spatially dependent coexistence state and permanence effect of the ecological system. Numerical simulations are provided to corroborate theoretical results and to illustrate dynamic transitions from extinction or single-dominance to stable coexistence. |
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