4. Formal Spiking Neuron Models

Detailed conductance-based neuron models can reproduce electrophysiological
measurements to a high degree of accuracy, but because of their intrinsic
complexity these models are difficult to analyze. For this reason, simple
phenomenological spiking neuron models are highly popular for studies of
neural coding, memory, and network dynamics. In this chapter we discuss
formal threshold models of neuronal firing. Spikes are generated whenever the
membrane potential *u* crosses some threshold from below. The
moment of threshold crossing defines the firing time *t*^{(f)},

Since spikes are stereotyped events they are fully characterized by their firing time. We focus on models that are based on a single variable

- 4.1 Integrate-and-fire model
- 4.1.1 Leaky Integrate-and-Fire Model
- 4.1.2 Nonlinear integrate-and-fire model
- 4.1.3 Stimulation by Synaptic Currents

- 4.2 Spike response model (SRM)
- 4.2.1 Definition of the SRM
- 4.2.2 Mapping the Integrate-and-Fire Model to the SRM
- 4.2.3 Simplified Model SRM
_{0}

- 4.3 From Detailed Models to Formal Spiking Neurons
- 4.3.1 Reduction of the Hodgkin-Huxley Model
- 4.3.2 Reduction of a Cortical Neuron Model
- 4.3.3 Limitations

- 4.4 Multi-compartment integrate-and-fire model
- 4.4.1 Definition of the Model
- 4.4.2 Relation to the Model SRM
_{0} - 4.4.3 Relation to the Full Spike Response Model (*)

- 4.5 Application: Coding by Spikes
- 4.6 Summary

Cambridge University Press, 2002

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