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October  2017, 10(5): 1165-1174. doi: 10.3934/dcdss.2017063

## 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

Received  September 2016 Revised  January 2017 Published  June 2017

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

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.

Citation: Shubo Zhao, Ping Liu, Mingchao Jiang. Stability and bifurcation analysis in a chemotaxis bistable growth system. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1165-1174. doi: 10.3934/dcdss.2017063
##### References:

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##### References:
Basic phase portrait of (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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