All Outputs (4)

Combining spatial and parametric working memory in a dynamic neural field model (2016)
Journal Article
Wojtak, W., Coombes, S., Bicho, E., & Erlhagen, W. (in press). Combining spatial and parametric working memory in a dynamic neural field model. Lecture Notes in Artificial Intelligence, 9886, https://doi.org/10.1007/978-3-319-44778-0_48

We present a novel dynamic neural field model consisting of two coupled fields of Amari-type which supports the existence of localized activity patterns or “bumps” with a continuum of amplitudes. Bump solutions have been used in the past to model spa... Read More about Combining spatial and parametric working memory in a dynamic neural field model.

Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function (2016)
Journal Article
Coombes, S., & Thul, R. (2016). Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function. European Journal of Applied Mathematics, 27(6), 904-922. https://doi.org/10.1017/S0956792516000115

The master stability function is a powerful tool for determining synchrony in high-dimensional networks of coupled limit cycle oscillators. In part, this approach relies on the analysis of a low-dimensional variational equation around a periodic orbi... Read More about Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function.

Neural field models with threshold noise (2016)
Journal Article
Thul, R., Coombes, S., & Laing, C. R. (2016). Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6, Article 3. https://doi.org/10.1186/s13408-016-0035-z

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate funct... Read More about Neural field models with threshold noise.

Mathematical frameworks for oscillatory network dynamics in neuroscience (2016)
Journal Article
Ashwin, P., Coombes, S., & Nicks, R. (2016). Mathematical frameworks for oscillatory network dynamics in neuroscience. Journal of Mathematical Neuroscience, 6, Article 2. https://doi.org/10.1186/s13408-015-0033-6

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting nov... Read More about Mathematical frameworks for oscillatory network dynamics in neuroscience.