THEORY OF SELF-ORGANIZATION OF CORTICAL MAPS - MATHEMATICAL FRAMEWORK

We have constructed a general theory describing cortical map formation in the primary sensory cortices by using three main hypotheses: (1) competition among synapses due to the limitation of a postsynaptic factor secretion, (2) synaptic stabilization which takes place by a presynaptic factor secretion, and (3) synaptic stabilization according to a local Hebbian rule. Based on these hypotheses, we have expressed a process of synaptic stabilization in terms of a nonlinear dynamical equation. From detailed consideration of this equation, we have found that the problem for cortical map formation is equivalent to that for the thermodynamics in the Potts spin system whose spin variables typically have complex internal states. This equivalence means that the developmental process of the central nervous system is the dynamical process near equilibrium. Furthermore, we can systematically deal with various cortical map formations within a unified framework of the thermodynamics. Therefore, we can interpret use-dependent self-organization of a cortical map as a kind of phase transition phenomena. Finally we can suggest that there exists a relationship among plasticity, effective temperature, presynaptic factor secretion and critical period. © 1990.