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- Open Access
Persistent localized activity in a two-population neural-field model with spatio-temporal external input
© Yousaf et al; licensee BioMed Central Ltd. 2011
- Published: 18 July 2011
- Differential Equation
- Neural Network
- Animal Model
- Time Evolution
- Ordinary Differential Equation
Persistent localized activity in neural networks has been suggested to serve as the neural substrate of short-term memory . Neural-field models  provide a powerful tool to study the existence, uniqueness and stability of this type of activity. Bump solutions are often considered as an example of localized activity. In , it has been shown that a two-population neural-field model (Fig.1A) exhibits up to two coexisting bump-pair solutions in the presence of homogeneous external input (or in the absence of external input). Here, we show that the same system can generate up to four coexisting bump pairs if the external input is spatially localized.
In general, neural-field models are formulated in terms of Volterra-equation systems or systems of integro-differential equations. The dynamics of bump (pulse) solutions is often studied in a simplified framework by means of ordinary differential equations describing the time evolution of the pulse widths (Amari approach, see ).
We determine fixed-point solutions and their stability analytically and illustrate the results by means of numerical simulations. Further, we numerically show that persistent localized activity in a two-population neural-field model can be switched on and off by means of brief external-input pulses localized in space in and time (see Fig 1B).
Supported by the Research Council of Norway (eVITA [eNEURO], Notur).
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