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arXiv · 2608.16052

Diffusion contrast induced dynamics in a time-periodic competition-diffusion system with equal total resources

Zhenzhen Li·Mingxin Wang
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Abstract

This paper investigates a time-periodic, spatiotemporally heterogeneous competition-diffusion system, where two species have different intrinsic growth rates but equal total resources per period. Using asymptotic analysis and principal eigenvalue theory, we systematically examine its dynamics. When both diffusion rates are small, spatial heterogeneity of the difference in time-averaged resources leads to uniform persistence, stable coexistence, and asymptotic spatial segregation; whereas its spatial uniformity produces multiple regimes--fast-diffuser selection, parameter-dependent coexistence, or slow-diffuser dominance--separated by smooth threshold curves under different structural conditions. In the regime where at least one diffusion rate is large, we obtain a detailed classification of the local dynamics, with sharp delineation of parameter regions for stable coexistence, competitive exclusion, and a novel bistable scenario, where both semi-trivial periodic solutions are linearly stable while an unstable coexistence state also exists. We further characterize the asymptotic profiles of positive solutions in the mixed-scale diffusion limit. Our results show that the interplay between temporal periodicity and spatial heterogeneity can overturn the classical "slower diffuser always prevails" principle, leading to a substantially richer range of ecological outcomes.

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Zhenzhen Li, Mingxin Wang. 2026-08-17. Diffusion contrast induced dynamics in a time-periodic competition-diffusion system with equal total resources. https://arxiv.org/abs/2608.16052

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