Abstract
We analyze a resource based competition model with diffusion where two competing species share a common resource, explicitly incorporating resource dynamics and intraspecific competition unlike classical Lotka–Volterra systems. We establish local and global stability conditions for all equilibria, showing that species survival depends on both competition strength and resource availability, with intraspecific competition critically stabilizing the system to enable coexistence. The model exhibits Turing pattern formation when intraspecific competition is present, a phenomenon that is absent in classical competition models. Numerical simulations reveal traveling waves, territorial formation, and complex spatiotemporal dynamics. These results highlight how resource limitations and self-regulation shape competitive outcomes in spatial environments, with important implications for conservation and ecosystem management.
•Stabilizing Effect of Intraspecific Competition: We rigorously establish that intraspecific competition transforms unstable interior equilibria into locally asymptotically stable states, providing a mathematical foundation for the ecological principle that self-limitation promotes biodiversity.•Turing Pattern Formation: The model exhibits Turing instability, leading to the spontaneous emergence of spatial patterns, a phenomenon absent in classical competition models.•Complex Spatiotemporal Dynamics: Numerical simulations reveal traveling waves, territorial formation, and stable spatial segregation, offering insights into how competing species achieve coexistence. refugia.•Global Stability Analysis: We provide comprehensive local and global stability conditions for all equilibria, highlighting the interplay between resource availability,