Brain dynamics through spectral-structural neuronal networks

Starting from the morphological-functional assumption of the fractal brain, a mathematical model is given by activating brain’s non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms. The postulation of a scale covariance principle in Schrödinger’s type representation of the brain geodesics implies the spectral functionality of the brain dynamics through mechanisms of tunelling, percolation etc., while in the hydrodynamical type representation, it implies their structural functionality through mechanisms of wave schock, solitons type etc. For external constraints proportional with the states density, the fluctuations of the brain stationary dynamics activate both the spectral neuronal networks and the structural ones through a mapping principle of two distinct classes of cnoidal oscillation modes. The spectral-structural compatibility of the neuronal networks generates the communication codes of algebraic type, while the same compatibility on the solitonic component induces a strange topology (the direct product of the spectral topology and the structural one) that is responsible of the quadruple law (for instance, the nucleotide base from the human DNA structure). Implications in the elucidation of some neuropsychological mechanisms (memory’s location and functioning, dementia etc.) are also presented. Keyword: communication languages; codes; brain; coherence; neuronal network.