State-changes in the brain viewed as linear steady-states and non-linear transitions between steady-states

Preceding papers concern a linear theory of electrocortical waves and their regulation by brain-stem neurones, in conditions of steady-state. The present paper reconsiders the theory, and generalizes beyond the effects of the fibre systems so far studied. Relaxation and unification of the assumptions upon which the initial model was based is undertaken. It is shown that the generalised model may render state changes within the brain accessible to systematic description, using the EEG as dependent variable. It is proposed that a multitude of stable states are possible within the brain, each characterised by a set of damping parameters for separate linear resonant modes. Within each stable state, the set of sums of resonant modes characterises a sub-space of the total state-space. Transition between stable regions can occur with either perturbation by external signals, or by internal controls. Tentative consideration is given to the role of plastic changes leading to adaptive learning as an attribute of a system of this type.