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Sensitivity to initial conditions is usually associated with chaotic dynamicsand strange attractors. However, even systems with (quasi)periodic dynamics canexhibit it. In this context we report on the fractal properties of theisochrons of some continuous-time asymptotically periodic systems. We define aglobal measure of phase sensitivity that we call the phase sensitivitycoefficient and show that it is an invariant of the system related to thecapacity dimension of the isochrons. Similar results are also obtained withdiscrete-time systems. As an illustration of the framework, we compute thephase sensitivity coefficient for popular models of bursting neurons,suggesting that some elliptic bursting neurons are characterized by isochronsof high fractal dimensions and exhibit a very sensitive (unreliable) phaseresponse.

Extreme phase sensitivity in systems with fractal isochrons