Let u 1 and u 2 be the respective responses in some system. And lastly, let c be any constant. Any system which is not linear. The following MPEG file illustrates nonlinearity in a model of cell electrical activity. Excitable Systems and Excitability Excitability is not a mathematical term.
Nerve cells are classic examples of excitable systems though there are chemical ones as well.
Typically in excitable systems, even larger super threshold responses do not ellict an even larger response. The following MPEG illustrates stable equilibria and periodic solutions in an activator-inhibitor system with two chemical species. The bottom panel shows an approach to a stable equilibria. Notice that in the periodic case, the resulting periodic solutions are out of phase but otherwise identical. To clearly illustrate this, it is often useful to graph the concentrations against each other.