Oscillatory Neural Networks

Abstract

Oscillatory neural networks are found throughout the nervous system. They are responsible for many repetitive motor activities and have recently been shown to play a role in cognition. In spite of the many different mechanisms that underlie neural oscillations, they can be understood using a common mathematical framework. Most neural oscillators arise from slow or delayed negative feedback. The timing of groups of oscillators depends both on the arrangement of their connections and their intrinsic properties and, in particular, on their phase resetting curve. Linear chains of oscillators can produce travelling waves, and these waves control undulatory movement in many animals. There are many mechanisms for generating waves in a chain including asymmetry in coupling, heterogeneities and pacemakers.

Key Concepts:

  • The mechanisms for the creation of neural oscillators generally involve delayed negative feedback.

  • Coordination of neural oscillations occurs through coupling that can take many forms including direct electrical coupling and chemical synaptic transmission.

  • The phase‚Äźresponse curve of an oscillator shows how perturbations shift to timing and how the oscillator responds to stimuli.

  • The timing patterns produced by networks of oscillators depend on the nature of the coupling, the internal dynamics of the oscillator and the connectivity pattern.

  • Metachronal waves, for example, found in the swimming of the lamprey or the leech can be viewed as a chain of coupled neural oscillators item. Cortical oscillations may play a role in attention and enhancement of sensory coding. However, unlike the simple CPGs described in most of this article, the role of rhythms in higher brain regions remains controversial and is not yet settled.

Keywords: rhythms; inhibition; synchrony; central pattern generators; neural oscillator; nonlinear dynamics

Figure 1.

Three mechanisms for oscillations. (a) Delayed negative feedback, (b) positive feeback or substrate depletion, (c) reciprocal excitatory/inhibitory coupling between excitable elements.

Figure 2.

Interactions between four oscillators that produce different quadruped gaits.

Figure 3.

A canonical circuit for the production of metachronal waves. Typically, the CPG consists of two chains (left and right) that are reciprocally coupled. The coupling up and down is generally much more complex and asymmetric. Various schemes are described in the text.

Figure 4.

Model for cortical gamma rhythm. One hundred inhibitory cells that fire at different rates are coupled with a combination of inhibitory synapses and gap junctions. Top shows the power spectra for the uncoupled (red), synaptically coupled (green) and a mix of synaptic and electrical coupling (black). Corresponding spiking activity of the neurons is shown below with each dot corresponding to an action potential.

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References

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Further Reading

Glass L and Mackey M (1988) From Clocks to Chaos: The Rhythms of Life. Princeton, NJ: Princeton University Press.

Goldbeter A (1996) Biochemical Oscillations and Cellular Rhythms. Cambridge, UK: Cambridge University Press.

Koch C and Segev I (eds) (1998) Methods in Neuronal Modeling (see particularly chapters 7,10) Cambridge, MA: MIT Press.

Winfree AT (1980) The Geometry of Biological Time. New York: Springer‐Verlag.

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How to Cite close
Ermentrout, G Bard(Jan 2011) Oscillatory Neural Networks. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0000276.pub2]