Spreading speeds for a Lotva-Volterra competition system with advection in a periodic habitat

Abstract

The study investigates pulsating wave speeds in an advective two-species competition-diffusion system under periodic environments. Recent studies have confirmed the existence and characterized the qualitative dynamics of pulsating waves. In this paper, we determine pulsating wave speed’s signs with identical diffusion rates and characterize invasion dynamics of competing species in heterogeneous environments by comparing the reactions and competitions. Specifically, we first establish a criterion for zero-speed waves and derive sufficient conditions for strictly positive or negative speeds. Our framework extends previous studies (e.g., Ding and Liang, Math. Ann. 385 (2023), 1–36) by considering functional representation of periodic steady-state solutions and explicit inclusion of advection effects and extends (e.g., Du et al., Z. Angew. Math. Phys. 71 (2020), 27 pp.) by further considering the sign of the pulsating wave speed, determining the long-time behavior of two strongly competing species. Crucially, the presence of the advection term indeed exerts a certain influence on the long-time behavior of two strongly competing species: From the perspective of the proof process, the appearance of the advection term increased the difficulty and complexity of proving Lemmas 2.3 and 3.1; from the result perspective, the advection term necessitates specific structural conditions for definitive speed determination. These findings advance understanding of pattern selection mechanisms in flow-driven ecological systems.