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Spatiotemporal instabilities in neural fields and the effects of additive noise

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Modeling Phase Transitions in the Brain

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 4))

Abstract

The spatiotemporal activity of neural populations may be measured by various experimental techniques. To understand the underlying dynamics of such an observed activity, it is important to study neural population models extended in space. A well-studied mesoscopic population model is the neural field, which assumes a continuous space and may involve various spatial axonal interactions, axonal temporal and spatiotemporal delays, various synaptic time-scales and external inputs. This chapter shows the analysis steps of such a neural field model, allowing deeper insight into the activity of neural populations. After the derivation of the model and its relation to physiology, the first analysis step investigates the linear stability of the system activity about a stationary state. In this context, time-independent and time-dependent phase transitions subject to axonal conduction delay are discussed analytically and numerically. In a subsequent analysis step, the stability and linear response theory in the presence of noisy inputs is discussed. Finally, the linear study of noisy phase transistions is extended to a nonlinear treatment, and nonlinear effects of additive noise are discussed analytically and numerically.

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  1. LORIA, Campus Scientifique-BP 239, 54506, Vandoeuvre-Les-Nancy Cedex, France

    Axel Hutt

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  1. Axel Hutt
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Correspondence to Axel Hutt .

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  1. Dept. Engineering, University of Waikato, Hillcrest Road, Hamilton, 3240, New Zealand

    D. Alistair Steyn-Ross

  2. Dept. Engineering, University of Waikato, Hillcrest Road, Hamilton, 3240, New Zealand

    Moira Steyn-Ross

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Hutt, A. (2010). Spatiotemporal instabilities in neural fields and the effects of additive noise. In: Steyn-Ross, D., Steyn-Ross, M. (eds) Modeling Phase Transitions in the Brain. Springer Series in Computational Neuroscience, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0796-7_3

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