Stability and Bifurcation Analysis in a System of Four Coupled Neurons with Multiple Delays

A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the s...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2013-04, Vol.29 (2), p.425-448
Main Authors: Li, Xiu-ling, Wei, Jun-jie
Format: Article
Language:English
Subjects:
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
分岔分析
参数空间
多时滞系统
延迟微分方程
时间延迟
神经元模型
稳定性
耦合
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Summary:A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-013-0212-8