1. Propagation dynamics of nonlocal dispersal competition systems in time-periodic shifting habitats.
- Author
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Qiao, Shao-Xia, Li, Wan-Tong, and Wang, Jia-Bing
- Subjects
- *
CAUCHY problem , *HABITATS , *TRAFFIC safety , *HAMILTONIAN systems , *ANIMAL dispersal - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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