Continuum models in neurobiology and information processing

Abstract

Continuum models have been used with considerable success for single neurons but have been neglected in the study of neuronal populations. In more popular discrete neuronal network models, the geometric details of the neuronal centers are usually neglected. We here give a continuum nonlinear dynamical model and an approximate model which admits the possibility of ascertaining the roles of the various connectivity patterns from center to center in the central nervous system. Frequency transfer characteristics are used to incorporate the nonlinear dynamics of single neurons. Simple examples are evaluated both analytically and numerically and the results presented graphically.