Collective dynamics, control and imaging

Excitable behaviors

Rodolphe Sepulchre

University of Cambridge
[SLIDES]

Excitability is a core property of biological processes but the mathematical theory of excitability is at best scarce. The talk will discuss excitability as a system theoretic concept. After a brief review of the landmark work of Hodgkin and Huxley, I will discuss limitations of studying excitability through the mathematical theory of nonlinear differential equations. The main focus will be to illustrate that excitability is a system property, regulated by feedback, and to motivate a system theoretic approach to the analysis and design of excitable networks. It will be argued that excitability is central to developing a theory of control across scales.