Journal
NONLINEAR DYNAMICS
Volume 76, Issue 1, Pages 115-124Publisher
SPRINGER
DOI: 10.1007/s11071-013-1114-2
Keywords
Stability; Reaction-diffusion; Turing instability; Amplitude equations; Neural networks
Categories
Funding
- National Natural Science Foundation of China [61174155, 11032009]
- Qing Lan Project of Jiangsu
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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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