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

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.