Dynamic Pattern Formation Leads to $\frac{1}{f}$ Noise in Neural Populations

We present a generic model that generates long-range (power-law) temporal correlations, $\frac{1}{f}$ noise, and fractal signals in the activity of neural populations. The model consists of a two-dimensional sheet of pulse coupled nonlinear oscillators (neurons) driven by spatially and temporally uncorrelated external noise. The system spontaneously breaks the translational symmetry, generating a metastable quasihexagonal pattern of high activity clusters. Fluctuations in the spatial pattern cause these clusters to diffuse. The macroscopic dynamics (diffusion of clusters) translate into $\frac{1}{f}$ power spectra and fractal (power-law) pulse distributions on the microscopic scale of a single unit.