The Complexity in Activity of Biological Neurons

Abstract

We sum up our work about neurodynamics in this chapter. It is widely considered that the nervous system in man and animals is a rather complicated nonlinear dynamical system. Therefore, it is both necessary and important to understand the behavior occurred in the nervous system from the perspective of nonlinear dynamics. Actually, a great many of novel and puzzling phenomena are just observed in a single neuron, but their physiological or dynamical mechanisms remain open so far. In other words, single neurons are not simple. We show many firing patterns in theoretical neuronal models or neurophysiological experiments of single neurons in rats in this chapter. And then we introduce three representative examples of best known mathematical neuron models. The two types of neuronal excitability are illustrated by the Hodgkin-Huxley mode and the Morris-Lecar model. Especially, it is shown that we can change the types of neuronal excitability using the methods of bifurcation control. Besides, we display bursting and its topological classification, and explain bifurcation, chaos and crisis by the existing neuronal models. We give emphasis to sensitive responsiveness of aperiodic firing neurons to external stimuli, and show experimental phenomena and their underlying nonlinear mechanisms. The synchronization between neurons is remarked simply. We stress a constructive role of noise in the nervous system, and depict the phenomena of stochastic resonance and coherence resonance, and give their dynamical mechanisms. The common analysis methods are presented for the time series of the interspike intervals. Finally, we give two application examples about controlling chaos and stochastic resonance, and draw some conclusions.