Dynamical Systems in Neuroscience:

Bursting 387spiking(a)Vfastnfoldthresholdhomoclinicrestingn slow(b)stimulationstimulationstimulation(c)stimulationFigure 9.48: Bistability of resting and spiking states in a “fold/homoclinic” burster. Abrief stimulus can initiate a premature transition to spiking state (b) or to quiescentstate (c). Shown are simulations of the I Na,p +I K +I K(M) -model with parameters as inFig. 9.4b.9.4.4 Bursts as a unit of neuronal informationMammalian neurons may fire bursts to increase the reliability of synaptic transmission(Lisman 1997). Indeed, if a presynaptic neuron sends a burst of spikes instead of a singlespike, then the chances that at least one of them overcomes the synaptic transmissionfailure increase. If two or more spikes go through, then the postsynaptic effect is muchstronger than the one for a single spike.In addition, important information may be carried in the intraburst frequency.Consider the effect of a burst on a postsynaptic resonator neuron, i.e., a neuron withresting state near an Andronov-Hopf bifurcation. Such a neuron cares about the frequencycontent of the burst, i.e., whether it is resonant or not, as we discussed inSect. 7.2.2. Some types of bursters have relatively constant intraburst (instantaneousinterspike) frequencies, as in Fig. 9.49b, which may be resonant for some postsynaptic