Differential and Integral Equations

On stability of traveling wave solutions in synaptically coupled neuronal networks

Linghai Zhang

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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.

Article information

Source
Differential Integral Equations, Volume 16, Number 5 (2003), 513-536.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060624

Mathematical Reviews number (MathSciNet)
MR1973060

Zentralblatt MATH identifier
1034.45012

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 35B35: Stability 35R10: Partial functional-differential equations 92C20: Neural biology

Citation

Zhang, Linghai. On stability of traveling wave solutions in synaptically coupled neuronal networks. Differential Integral Equations 16 (2003), no. 5, 513--536. https://projecteuclid.org/euclid.die/1356060624


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