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Fig. 3 Cloud bursting model.

They also implemented a slow-wave bursting model.

Either bursting model falls into a class of dynamical systems with at least two time scales, known as slow-fast systems.

We simulated the activity of a bursting model neuron (see Methods and Figure 2A) driven by a time-dependent signal that is proportional to the LFP.

This is consistent with the exact results obtained by us earlier for a simple bursting model [ 24].

At large times the Fano factor settles to the steady-state value for a bursting model that toggles between the enhanced and basal production rates.

This creates a mechanism for spike adding [19] in bursting models [9, 20 26].

This is similar to neuronal bursting models perturbed by noise [36].

The critical manifold in bursting models with one slow and two fast variables is a one-dimensional manifold of equilibrium points of the fast subsystem, and it often takes a cubic shape.

The presence of intrinsic oscillations complicates the case of continuous inputs, because the impact of an input will depend on the phase at which it starts, as in recent phase resetting analysis for bursting models [18, 19].

Nonetheless, this approach has a long history of providing powerful insights, for example, in work ensuing from the classical dissection of minimal bursting models by [16] and in the study of coupled neuronal oscillators and bursters (e.g, [17 20] and many others since).