Dynamical Systems in Neuroscience:

Bursting 343Figure 9.2: Is bursting a spiking state interrupted by periods of quiescence or is it aquiescent state interrupted by groups of spikes?V(t)20 mV50 msI(t)Figure 9.3: Forced bursting in the I Na,p +I K -model with parameters as in Fig. 4.1a andtime-dependent injected current I(t).quiescent phase. Before proceeding to a general case, let us consider a simple example.9.1.1 Example: The I Na,p +I K +I K(M) -modelAny model neuron capable of spiking can also burst, as e.g., the I Na,p +I K -model inFig. 9.3. However, this example is not interesting because the neuron is forced to burstby the time-dependent input I(t).In contrast, a modification of the I Na,p +I K -model in Fig. 9.4 fires a burst of spikesin response to a brief pulse of current. The first spike in the burst is caused by thestimulation, but the subsequent spikes are generated autonomously due to the intrinsicproperties of the neuron, and they outlast the stimulation. Such a burst is stereotypicaland fairly independent of the amplitude or the duration of the pulse that triggered it.To make the I Na,p +I K -model burst, we took parameters as in Fig. 6.7a, so that