43. chen.ruau.ea:26:chemotaxis#
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
Le Chen, Ian Ruau, and Wenxian Shen
Abstract: Part II of the series on chemotaxis models with signal-dependent sensitivity and a logistic-type source. We prove uniform persistence when \(m \ge 1\), identify the linear stability threshold \(\chi^*(u^*)\) of the positive equilibrium, give conditions for exponential convergence to it, and treat the mass-constrained case \(a=b=0\). Signal saturation (large \(\beta\)) or repulsion (\(\chi_0<0\)) prevents aggregation and promotes relaxation.
[CRS26a] Le Chen, Ian Ruau & Wenxian Shen (2026) ‘Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization’, preprint arXiv:2604.02599, 51 pages
@article{chen.ruau.ea:26:chemotaxis,
title = {Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization},
author = {Le Chen and Ian Ruau and Wenxian Shen},
year = {2026},
month = {April},
journal = {Preprint arXiv:2604.02599},
url = {http://arXiv.org/abs/2604.02599}
}