Self-similar characteristics of neural networks based on Fokker–Planck equation

✍ Scribed by Yoshinobu Kamitani; Ikuo Matsuba

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 332 KB
• Volume: 20
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(03)00388-6

✦ Synopsis

The ubiquity of 1=f type long memory processes has not been generally explained. One of the examples is found in electroencephalogram. Using simplified neural networks, we find a self-similar solution exhibiting 1=f spectra theoretically and experimentally. By coarse-graining the basic equation based on renormalization group equations, we derive 1=f from the network models. In the present paper, we do not only show the solution that leads to 1=f spectra, but also, employing the Fokker-Planck equation, we discuss the stability of the self-similar solution on our network models.