Two-frequency self-oscillations in a FitzHugh–Nagumo neural network
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- 作者：S. D. Glyzin ; A. Yu. Kolesov ; N. Kh. Rozov
- 关键词：FitzHugh–Nagumo neural network ; normal form ; invariant torus ; asymptotic behavior ; stability ; buffer phenomenon
- 刊名：Computational Mathematics and Mathematical Physics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：57
- 期：1
- 页码：106-121
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Computational Mathematics and Numerical Analysis;
- 出版者：Pleiades Publishing
- ISSN：1555-6662
- 卷排序：57
文摘
A new mathematical model of a one-dimensional array of FitzHugh–Nagumo neurons with resistive-inductive coupling between neighboring elements is proposed. The model relies on a chain of diffusively coupled three-dimensional systems of ordinary differential equations. It is shown that any finite number of coexisting stable invariant two-dimensional tori can be obtained in this chain by suitably increasing the number of its elements.