Propagation dynamics of nonlocal dispersal competition systems in time-periodic shifting habitats

• Published in: Journal of Differential Equations 2024-01, Vol.378, p.399-459
• Main Authors: Qiao, Shao-Xia, Li, Wan-Tong, Wang, Jia-Bing
• Format: Article
• Language: English
• Subjects: Nonlocal dispersal competition system; Periodic forced waves; Spreading properties; Time-periodic shifting habitat
• ISSN: 0022-0396; 1090-2732
• DOI: 10.1016/j.jde.2023.09.027

This paper is concerned with the propagation dynamics of the time periodic Lotka-Volterra competition systems with nonlocal dispersal in a shifting habitat. We first obtain three types of time-periodic forced waves connecting the extinction state to the co-existence state, itself and the semi-trivial state, which describe the conversion from the state of two aboriginal co-existent competing species, two invading alien competitors, and a saturated aboriginal competitor with another invading alien competitor to the extinction state, respectively. This provides a comprehensive explanation of the point-wise extinction dynamics of these two competing species under such a time-periodic worsening habitat. Then, we establish the spreading properties of the associated Cauchy problem depending on the range of the shifting speed. More specifically, we give a complete description on the threshold values for the extinction as well as persistence (by moving with asymptotic speed). Our results reveal the possibility that a competitively weaker species with a much faster spreading speed can drive a competitively stronger species with a slower spreading speed to extinction. The discussion in this paper applies to both cases of weak competition and strong-weak competition. In particular, we need to point out that some combined effects of nonlocal dispersal, two-variable coupling and time-periodic shifting heterogeneity in this system pose extra difficulties in mathematical treatment, which are dealt with by introducing new approaches.