Bifurcation analysis provides theoretical guidelines and a powerful analytical framework to tune the activity of neuronal models. A bifurcation is a qualitative change in the activity of a dynamical system, such as a transition from silence to spiking. Bifurcation analysis identifies general dynamical laws governing transitions between activity regimes in response to changes in controlling parameters. By using these quantitative laws, the temporal characteristics of a neuronal model can be tuned to reproduce the characteristics of experimentally recorded activity by navigating the parameter space in the vicinity of bifurcations. In most of the bifurcations described here, the general shape of the waveform – for example, the shape of action potentials in a time series – is preserved, while a specific temporal characteristic changes.
KeywordsPeriodic Orbit Spike Activity Bifurcation Analysis Bifurcation Parameter Burst Duration
This work was supported by National Science Foundation grant PHY-0750456.
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