
The Second International
Conference: Nonlinear WavesTheory and Applications 
Nonlinear signaling in neurons and networks of neurons 
William L. Kath 
Northwestern University, U.S.A. 

Abstract: 
With its estimated 100 billion neurons and 200 trillion interconnections, the human central nervous system is one of the most
complex systems known. How does this collection of neurons transmit and process information? This tutorial will explain the basic biophysics of neurons and mathematical
models that describe how they actively signal one another. It will begin with a characterization of the membrane properties of neurons in terms of ordinary differential
equations and how these properties combine to produce the principal neuronal signal known as the action potential. This will be followed by a discussion of the partial differential
equation that describes the spread of voltage through the different parts of a neuron (e.g., the dendrites and axon) and its solution. It will finish with a mathematical description of chemical
and electrical signaling between neurons, and how this signaling leads to the larger networks of neurons capable of performing more sophisticated operations. 

