Nonlinear Dynamics of Small Neural Assemblies

Henry Abarbanel, UC San Diego

Using analysis tools from nonlinear systems, we show how to identify chaotic behavior in the membrane voltage recordings of individual neurons in an assembly of neurons found in the California spiny lobster. The analysis points to a failure in previous biologically based models of these neurons, and using this kind of clue, we show how to construct a class of neural models which do capture the nonlinear dynamics of this class of neurons.

We discuss limitations of the method and challenges in further analysis of both low and high dimensional chaotic systems.