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Turing instability and pattern formation of neural networks with reaction–diffusion terms

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Abstract

In this paper, a model for a network of neurons with reaction–diffusion is investigated. By analyzing the linear stability of the system, Hopf bifurcation and Turing unstable conditions are obtained. Based on this, standard multiple-scale analysis is used for deriving the amplitude equations of the model for the excited modes in the Turing bifurcation. Moreover, the stability of different patterns is also determined. The obtained results enrich the dynamics of neurons’ network system.

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Acknowledgements

We would like to express our gratitude to the referee for his or her valuable comments and suggestions that led to truly significant improvement of the manuscript. This research is supported by the National Natural Science Foundation of China (Nos. 61174155 and 11032009). The work is also sponsored by Qing Lan Project of Jiangsu.

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  1. Department of Mathematics, School of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hongyong Zhao, Xuanxuan Huang & Xuebing Zhang

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  1. Hongyong Zhao
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  2. Xuanxuan Huang
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  3. Xuebing Zhang
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Correspondence to Hongyong Zhao.

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Zhao, H., Huang, X. & Zhang, X. Turing instability and pattern formation of neural networks with reaction–diffusion terms. Nonlinear Dyn 76, 115–124 (2014). https://doi.org/10.1007/s11071-013-1114-2

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  • DOI: https://doi.org/10.1007/s11071-013-1114-2

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