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2003 On stability of traveling wave solutions in synaptically coupled neuronal networks
Linghai Zhang
Differential Integral Equations 16(5): 513-536 (2003).

Abstract

The author is concerned with the asymptotic stability of traveling wave solutions of integral differential equations arising from synaptically coupled neuronal networks. By using complex analytic functions, he proves that there is no nonzero spectrum of some linear operator $\mathcal L$ in the region Re $\lambda \geq 0$, and $\lambda =0$ is a simple eigenvalue. By applying linearized stability criterion, he shows that the traveling wave solutions are asymptotically stable. Additionally, some explicit analytic functions are found for a scalar integral differential equation.

Citation

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Linghai Zhang. "On stability of traveling wave solutions in synaptically coupled neuronal networks." Differential Integral Equations 16 (5) 513 - 536, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1034.45012
MathSciNet: MR1973060

Subjects:
Primary: 45K05
Secondary: 35B35, 35R10, 92C20

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 5 • 2003
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