Chaos by Probabilistic Cellular Automata

Marko Puljic, Computational Neurodynamics Laboratory Computer Science, University of Memphis

Electroencephalographic and magnetoencephalographic potential generated by active brain reveals widespread coherent oscillations. The oscillations of multiple rhythms overlap in broad spectrum noise. Spectrum analysis of short segments reveals peaks in the frequency ranges of the theta (3-7 Hz), alpha (8-12 Hz), beta (13-30), and gamma (30-100 Hz) bands. As the duration of segments chosen for analysis increases, the basic form to which spectra converge is the one of Brown noise. Any frequency can be modeled with probabilistic cellular automata. Coupled inhibitory and excitatory probabilistic cellular automata with appropriate topology and probabilistic rule governing the local interactions simulate an oscillator. Coupled oscillators create a model with the activation whose spectrum of long segments converges to a Brown noise.