Quaternion Dynamics of the Brain

In previous paper [1] an approach to nonlinear dynamical modeling of interaction between automatic (A) and conscious (C) processes in the brain was presented. The idea is to use complex field with real and imaginary components representing Aand C-processes. The interaction is due to the nonlinearity of the system. This approach was illustrated on the nonlinear equation for the current density in the cortex. The nonlinearity is determined by the sigmoidal firing rate of neurons. More general approaches were also indicated [1]. In this letter the quaternion (Q) approach is described. Subjective C-experiences can be divided into three major groups: sensations (S), emotions (E) and reflections (R). Note, that subjective S should be distinguished from the automatic sensory input into the neuron system of the brain. The effects of S, E and R on the electrochemical activity of the brain, generally, can be different. These effects should be distinguished in designing experiments and in C-modeling. The natural generalization of the approach [1] is to use the Q-field for representation of S-, Eand R-effects. Let us illustrate this on the model equation for the average (spatially uniform) current density α(t) perpendicular to the cortical surface [1]: