Chaotic dynamics in simple neuronal systems: theory and applications

The ubiquitous feature of the nervous system of wide spread occurrence of complex dynamics behaviour is treated. The cardinal question concerning the nature of generators of such complex behaviour, namely if it is ad hoc random or deterministic but strongly nonlinear, is analyzed. It is proved analytically that the discrete dynamics of single neurons with the sigmoidal transfer function is potentially chaotic. As the by-product the functional gain-threshold mechanism in neurons is derived. This allows for the new interpretations of famous experiments by Miyashita on squirell monkeys. Then it is shown that the continuous dynamics of the neural circuits of two-three neurons are endowed with the potentiality of chaotic firing, too. Finally, it will be argued that the classical dogma of stochastic or the ad hoc random neural coding can be taken as the limiting case of presenting new approach of deterministic or chaotic paradigm.