Stability and bifurcation analysis in a chemotaxis bistable growth system

Shubo Zhao; Ping Liu; Mingchao Jiang

doi:10.3934/dcdss.2017063

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2017, Volume 10, Issue 5: 1165-1174. Doi: 10.3934/dcdss.2017063

This issue Previous Article Dynamics and spatiotemporal pattern formations of a homogeneous reaction-diffusion Thomas model Next Article Global existence and energy decay estimate of solutions for a class of nonlinear higher-order wave equation with general nonlinear dissipation and source term

Stability and bifurcation analysis in a chemotaxis bistable growth system

Y. Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China

^* Corresponding author: Ping Liu
^* Corresponding author: Ping Liu

Received: September 2016

Revised: January 2017

Published: October 2017

Partially supported by NSFC grant 11571086,11471091 and Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province LC2013C01

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Abstract

The stability analysis of a chemotaxis model with a bistable growth term in both unbounded and bounded domains is studied analytically. By the global bifurcation theorem, we identify the full parameter regimes in which the steady state bifurcation occurs.

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Mathematics Subject Classification: 92C17, 74H60, 35B35, 35K55, 35K57.

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Figure 1. Basic phase portrait of (2)

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Figure 2. Parameter space for Turing instability. The parameter values are $d_1=d_2=f=g=1, \nu=\frac{1}{4}, $$ M=\frac{(\sqrt{d_1g}+\sqrt{(1-\nu)d_2})^2}{f}$

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