Neurons and Neural Networks: Computational Models

Horacio G Rotstein, New Jersey Institute of Technology, USA
Farzan Nadim, New Jersey Institute of Technology, USA

Published online: December 2007

DOI: 10.1002/9780470015902.a0000089.pub2

Neural networks produce electrical activity that is generated by the biophysical properties of the constituent neurons and synapses. Mathematical equations can be used to describe the electrical activity of neurons and neural networks and the underlying biophysical properties. These equations give rise to computational models of neurons and networks that can be analysed using mathematical techniques or numerically simulated with computers.

Keywords: nonlinear dynamics; bifurcation; phase plane; synchrony; membrane biophysics

Figure 1. Some common models of two-cell networks. (a) Synaptic inhibition is due to the release of a neurotransmitter that typically causes a negative change in the postsynaptic membrane potential. Two cells that are reciprocally coupled by synaptic inhibition can produce out-of-phase oscillatory activity (half-centre oscillation). (b) Synaptic excitation is caused by a neurotransmitter that typically produces a positive change in the postsynaptic potential. Two cells coupled with reciprocal excitation can oscillate in phase but the action potentials are not necessarily time-locked. (c) Electrical coupling is due to ion channels (gap-junctions) that span the membranes of two cells and allow free flow of ions between the two. Electrically coupled cells typically demonstrate synchronous activity, which may be oscillatory even if the two cells are not rhythmically active in isolation.
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Neurons | Neural Networks and Behaviour
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Article Title: Neurons and Neural Networks: Computational Models
 
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Rotstein, Horacio G, and Nadim, Farzan(Dec 2007) Neurons and Neural Networks: Computational Models. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0000089.pub2]