Differential and Integral Equations
- Differential Integral Equations
- Volume 16, Number 5 (2003), 513-536.
On stability of traveling wave solutions in synaptically coupled neuronal networks
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.
Differential Integral Equations, Volume 16, Number 5 (2003), 513-536.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 35B35: Stability 35R10: Partial functional-differential equations 92C20: Neural biology
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