Abstract
In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection.
Highlights
For researchers from the fields of biology and mathematics, advancing the exploration of dynamic systems is a long-term challenge
Li et al introduced the weighted Lyapunov functional related to the advection term to study global stability results in 2020, and studied the stability and bifurcation analysis of the model with the time delay term in 2021
Motivated by the efforts of the aforementioned papers, we will investigate the global stability of a non-homogeneous steady-state solution of a Lotka–Volterra model between two organisms in heterogeneous environments, where two competing organisms have different intrinsic growth rates, advection and diffusion strategies, and follow different positive diffusion distributions
Summary
For researchers from the fields of biology and mathematics, advancing the exploration of dynamic systems is a long-term challenge (see [1,2,3]). The competitive system of two diffusive organisms is often used to simulate population dynamics in biomathematics; for an example, see [1,2,4]. In 2020, by proposing a new Lyapunov functional, Ni et al [6] first studied and proved the global stability of a diffusive, competitive twoorganism system, and extended it to multiple organisms. Motivated by the efforts of the aforementioned papers, we will investigate the global stability of a non-homogeneous steady-state solution of a Lotka–Volterra model between two organisms in heterogeneous environments, where two competing organisms have different intrinsic growth rates, advection and diffusion strategies, and follow different positive diffusion distributions. Two bounded functions λ1(x) and λ2(x) are the intrinsic growth rates of competing organisms , ρ1(x), ρ2(x) ∈ C2(Ω) are two positive diffusion distributions, respectively.
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