arXiv subjects

Mihaela Negreanu

Publications and source records attributed to Mihaela Negreanu.

5 recordsLinked to original sources

arXiv2026

Transient instability and recurrent aggregation in a two-species chemotaxis-competition system under environmental periodicity

This work investigates recurrent pattern formation in a two--species chemotaxis system with competitive dynamics under the assumption that the carrying capacities of both species are periodic in time. By considering a globally attracting periodic solution to the associated nonautonomous ODE system as a spatially homogeneous base state, we derive sufficient conditions for the existence of a critical chemotactic sensitivity of the first species, denoted by $\chi_{\text{crit}}$. Whenever this threshold is exceeded, the periodic state becomes linearly unstable over a nonempty set of times within each environmental cycle. This gives rise to a recurrent alternation of unstable and stable intervals, during which spatial perturbations are respectively amplified and damped. The analytical derivation is complemented with numerical simulations, in both periodic coexistence and competitive exclusion regimes. Finally, we discuss the temporal location of the instability sets and the possibility of negative instability thresholds.

math.AP↗

arXiv2026

Global stability in a negative chemotaxis system with chemically induced lethality

In this paper, we investigate the long-time dynamics of a repulsive Keller-Segel chemotaxis system. The model features negative chemotaxis, logistic growth and a cell death term, accounting for a lethal chemorepellent that is self-produced by the cells and externally supplied. We prove that, for constant chemorepellent supplies, depending on their magnitude with respect to the logistic growth rate, solutions converge in $L^\infty$ norm toward extinction of the population, or equilibrate toward a nontrivial spatially homogeneous steady state.

math.AP↗

arXiv2025

Asymptotics and periodic dynamics in a negative chemotaxis system with cell lethality

This work studies the following system of parabolic partial differential equations \begin{equation*} \begin{cases} \displaystyle \frac{\partial u}{\partial t} = DΔu + χ\nabla \cdot(u \nabla v) + ru(1-u) - u v, \quad & x \in Ω, ~t > 0, \\ \displaystyle \frac{\partial v}{\partial t} = Δv + a u -v+ f(x,t), \quad & x \in Ω, ~t > 0, \end{cases} \end{equation*} modeling the negative chemotaxis interactions between a biological species and a lethal chemical substance that is supplied according to the known function $f(x,t)$. \\\\ It is shown that if $f$ converges to a spatially homogeneous function $\tilde{f}$ in a certain sense, then the solution $(u,v)$ satisfies $$ ||u-\tilde{u}||_{L^2(Ω)} + ||v-\tilde{v}||_{L^2(Ω)} \to 0 \quad \text{as } t \to \infty, $$ where $(\tilde{u},\tilde{v})$ is the solution to the associated ODE system \begin{equation*} \begin{cases} \displaystyle \frac{d \tilde{u}}{dt~} = r \tilde{u} (1 - \tilde{u}) - \tilde{u}\tilde{v}, \quad & t>0,\\ \displaystyle \frac{d \tilde{v}}{dt~} = a\tilde{u} - \tilde{v} + \tilde{f},\quad & t>0. \end{cases} \end{equation*} Some final remarks are given for the case in which $\tilde{f}$ is a time periodic function, and under which hypotheses do $(\tilde{u},\tilde{v})$ inherit this periodicity.

math.AP↗

arXiv2023

Convergence of a meshless numerical method for a chemotaxis system with density-suppressed motility

This article studies a parabolic-elliptic system modelling the pattern formation in E. coli bacteria in response to a chemoattractant known as acylhomoserine lactone concentration (AHL). The system takes into account certain bacterial strains with motility regulation, and the parameters of the equations represent the bacterial logistic growth, AHL diffusion and the rates of production and degradation of AHL. We consider the numerical solution to the system using the Generalized Finite Difference (GFD) Method, a meshless method known to effectively compute numerical solutions to nonlinear problems. The paper is organized to first explain the derivation of the explicit formulae of the method, followed by the study of the convergence of the explicit scheme. Then, several examples over regular and irregular meshes are given.

math.NA↗

arXiv2016

Constructing solutions for a kinetic model of angiogenesis in annular domains

We prove existence and stability of solutions for a model of angiogenesis set in an annular region. Branching, anastomosis and extension of blood vessel tips are described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions and coupled to a diffusion problem with Neumann boundary conditions through the force field created by the tumor induced angiogenic factor and the flux of vessel tips. Our technique exploits balance equations, estimates of velocity decay and compactness results for kinetic operators, combined with gradient estimates of heat kernels for Neumann problems in non convex domains.

math.AP↗