arXiv subjects

Weirun Tao

Publications and source records attributed to Weirun Tao.

4 recordsLinked to original sources

arXiv2025

Effects and biological consequences of the predator-mediated apparent competition I: ODE models

This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model with Holling type I and II functional response functions. Through the analytical results and case studies alongside numerical simulations, we find that the initial mass of the invasive prey species, capture rates of prey species, and the predator's mortality rate are all important factors determining the success/failure of invasions and the species coexistence/extinction. The global dynamics can be completely classified for the Holling type I functional response function, but can only be partially determined for the Holling type II functional response function. For the Holling type I response function, we find that whether the invasive prey species can successfully invade to promote the predator-mediated apparent competition is entirely determined by the capture rates of prey species. If the Holling type II response function is applied, then the dynamics are more complicated. First, if two prey species have the same ecological characteristics, then the initial mass of the invasive prey species is the key factor determining the success/failure of the invasion and hence the effect of the predator-mediated apparent competition. Whereas if two prey species have different ecological characteristics, say different capture rates, then the success of the invasion no longer depends on the initial mass of the invasive prey species, but on the capture rates. In all cases, if the invasion succeeds, then the predator-mediated apparent competition's effectiveness essentially depends on the predator's mortality rate.

q-bio.PE↗

arXiv2018

Boundedness and stabilization in a two-species chemotaxis system with signal absorption

This paper is concerned with the Neumann initial-boundary value problem for the two-species chemotaxis system with consumption of chemoattractant \begin{equation*} u_t=Δu-χ_1\nabla\cdot(u\nabla w), \end{equation*} \begin{equation*} v_t=Δv-χ_2\nabla\cdot(v\nabla w), \end{equation*} \begin{equation*} w_t=Δw-(αu+βv)w \end{equation*} in a smooth bounded domain $Ω\subset\mathbb{R}^n$ ($n\geq2$), where the parameters $χ_1$, $χ_2$, $α$ and $β$ are positive. It is proved that if \begin{equation*} \max\{χ_1,χ_2\}\|w(x,0)\|_{L^{\infty}(Ω)}<\sqrt{\frac{2}{n}}π\end{equation*} the problem possesses a unique global classical solution that is uniformly bounded. Moreover, we prove that \begin{equation*} u(x,t)\to\frac{1}{|Ω|}\int_Ωu(x,0),\quad v(x,t)\to\frac{1}{|Ω|}\int_Ωv(x,0)\quad\mbox{and}\quad w(x,t)\to0\quad\mbox{as}\ t\to\infty \end{equation*} uniformly with respect $x\inΩ$.

math.AP↗

arXiv2018

Global existence and boundedness in a chemotaxis-Stokes system with slow $p$-Laplacian diffusion

This paper deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow $p$-Laplacian diffusion \begin{equation}\nonumber \left\{ \begin{aligned} &n_t+u\cdot\nabla n=\nabla\cdot\left(|\nabla n|^{p-2}\nabla n\right)-\nabla\cdot(n\nabla c), &x\inΩ,\ t>0,\ \ &c_t+u\cdot\nabla c=Δc-nc,&x\inΩ,\ t>0,\ \ &u_t=Δu+\nabla P+n\nablaϕ,&x\inΩ,\ t>0,\ \ &\nabla\cdot u=0, &x\inΩ,\ t>0,\ \ \end{aligned} \right. \end{equation} where $ϕ\in W^{2,\infty}(Ω)$ is the gravitational potential. It is proved that global bounded weak solutions exist whenever $p>\frac{23}{11}$ and the initial data $(n_0,c_0,u_0)$ are sufficiently regular satisfying $n_0\geq 0$ and $c_0\geq 0$.

math.AP↗

arXiv2018

Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion

This paper investigates an incompressible chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion \begin{eqnarray} \left\{\begin{array}{lll} n_t+u\cdot\nabla n=\nabla\cdot(|\nabla n|^{p-2}\nabla n)-\nabla\cdot(nχ(c)\nabla c),& x\inΩ,\ t>0, c_t+u\cdot\nabla c=Δc-nf(c),& x\inΩ,\ t>0, u_t+(u\cdot\nabla) u=Δu+\nabla P+n\nablaΦ,& x\inΩ,\ t>0, \nabla\cdot u=0,& x\inΩ,\ t>0 \end{array}\right. \end{eqnarray} under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of Dirichlet type for $u$ in a bounded convex domain $Ω\subset \mathbb{R}^3$ with smooth boundary. Here, $Φ\in W^{1,\infty}(Ω)$, $0<χ\in C^2([0,\infty))$ and $0\leq f\in C^1([0,\infty))$ with $f(0)=0$. It is proved that if $p>\frac{32}{15}$ and under appropriate structural assumptions on $f$ and $χ$, for all sufficiently smooth initial data $(n_0,c_0,u_0)$ the model possesses at least one global weak solution.

math.AP↗