Bessel Functions in Mass Action. Modeling of Memories and Remembrances

Data from experimental observations of certain brain functions, such as impulse responses of cortex to electric shocks (average evoked potentials), related with the coexistence of pulses and wave modes in the dynamics of a class of neurological processes (Freeman K-sets), present functional distribution reproducing the Bessel function behavior. This suggests the possibility to replace ordinary differential equations, typically used to model data bases concerning such processes, with couples of damped/amplified oscillators which provide time dependent representation of spherical Bessel equation. The root loci of poles and zeros of the equation solutions are shown to conform to solutions of K-sets. One advantage of the present formalism is that some light is shed on the problem of filling the gap between the behavior at cellular level and the macroscopic dynamics involved in the traffic between the brain and its environment. Breakdown of time-reversal symmetry in each of the (damped and amplified) oscillators is related with the cortex thermodynamic features. This is proposed to be a possible mechanism to deduce lifetime of recorded memory.