Open AccessExistence and metastability of non-constant steady states in a Keller-Segel model with density-suppressed motility
Author(s) -
Peng Xia,
Yazhou Han,
Jicheng Tao,
Manjun Ma
Publication year - 2019
Publication title -
mathematics in applied sciences and engineering
Language(s) - English
Resource type - Journals
ISSN - 2563-1926
DOI - 10.5206/mase/8120
Subject(s) - metastability , constant (computer programming) , plane (geometry) , bifurcation , motility , phase plane , statistical physics , phase (matter) , stationary phase , physics , mathematics , mathematical analysis , chemistry , computer science , nonlinear system , biology , quantum mechanics , geometry , chromatography , genetics , programming language
We are concerned with stationary solutions of a Keller-SegelModel with density-suppressed motility and without cell proliferation. we establish the existence and the analytical approximation of non-constant stationary solutions by applying the phase plane analysis and bifurcation analysis. We show that the one-step solutions is stable and two or more-step solutions are always unstable. Then we further show that two or more-step solutions possess metastability. Our analytical results are corroborated by direct simulations of the underlying system.