Zero-crossing Pattern and Scaling of Background Brain Dynamics and Alpha Rhythm

The scaling property of the broad-band fluctuation and the $\alpha$ rhythm of the brain dynamics is studied based on the zero-crossing of the local electroencephalographic (EEG) recording taken from six healthy young adults in eyes closed and eyes open. A two-component scenario, consisting of a broad- band fractal and narrow-band rhythm components, is assumed to model the EEG zero-crossing. Scaling is found in the power law distribution $p(\tau)\sim\tau^{-\nu}$ of the crossing time interval $\tau$ of the broad-band fluctuation. An inverse relationship between broad-brand fluctuation and the $\alpha$ rhythm is observed. The Hurst exponent was found to be higher in eyes closed compared to eyes open. In $\alpha$ dominant brain state, the $\alpha$ rhythm interval $L$ also exhibits scaling in the form of power law distribution: $p(L)\sim L ^\phi$. Our main result is the relationship $\nu+\phi\sim 3$ that characterizes the ``organization'' of these two prominent features of the brain dynamics. The possible role of self- organized criticality of punctuated equilibrium in this organization is argued.