The nervous system as a collective of networks of non-linear dynamical systems
Dr. Alex Loebel
The nervous system is a complex of inter-connected networks, each of which is composed of local networks of interconnected units, or neurons. A neuron can be described essentially as a non-linear dynamical system; and the information transfer from one neuron to its contacts is mediated by non-linear junction points, called synapses. Even-though there has been great advances in the experimental techniques with which the nervous system is explored, the ability of measuring the activity from many neurons at the same time, and thus measure networks activity, is very much lacking. Much of our understanding, therefore, of biological neural networks originates from the study of the mathematical models of these networks.
In my talk, I will present the dynamical system of single neurons, that is, the Hodgkin-Huxley model, which is the basis of all the network models. I will then describe several key anatomical features of the nervous system, which imposes constraints on the models. Finally, I will discuss how connecting single neurons into different networks with different properties can explain important features of the nervous system, e.g., working memory.