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

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2019-09-30 DOI:10.5206/MASE/8120
Manjun Ma, Peng Xia, Yazhou Han, Jicheng Tao
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引用次数: 2

Abstract

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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具有密度抑制运动的Keller-Segel模型中非恒定稳态的存在性和亚稳态
我们关注的是Keller-Segel模型的固定解,该模型具有密度抑制的运动性且没有细胞增殖。利用相平面分析和分岔分析,建立了非常定常解的存在性和解析近似。我们证明了一步解是稳定的,两步或两步以上的解总是不稳定的。然后我们进一步证明了两个或两个以上的阶解具有亚稳性。我们的分析结果通过对底层系统的直接模拟得到了证实。
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来源期刊
CiteScore
1.40
自引率
0.00%
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0
审稿时长
21 weeks
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