Existence and metastability of non-constant steady states in a Keller-Segel model with density-suppressed motility | Zendy

Peng Xia | Zendy; Yazhou Han | Zendy; Jicheng Tao | Zendy; Manjun Ma | Zendy

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Existence 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.

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