Global dynamics of a classical Lotka–Volterra competition–diffusion–advection system
Abstrak
Abstract In this paper, we study a classical two species Lotka–Volterra competition–diffusion–advection system, where the diffusion and advection rates of two competitors are supposed to be proportional. By employing the principal spectral theory, we first establish a key a priori estimate on the co-existence (positive) steady state, which is a powerful tool to link the local and global dynamics. We then further present a complete classification on all possible long-time dynamical behaviors by appealing to the theory of monotone dynamical systems. Lastly, we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics. This work gives a positive answer to the conjecture proposed by Lou et al. in [34] by considering a more general model under certain conditions, and also, can be seen as a further development of He and Ni [19] for competition–diffusion system, where we bring new ingredients in the arguments to overcome the difficulty caused by the involvement of advection.
Topik & Kata Kunci
Penulis (2)
Peng Zhou
Dongmei Xiao
Akses Cepat
- Tahun Terbit
- 2018
- Bahasa
- en
- Total Sitasi
- 120×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1016/J.JFA.2018.03.006
- Akses
- Open Access ✓