Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

Peter Ashwin, Stephen Coombes, Rachel Nicks
2016 Journal of Mathematical Neuroscience  
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 novel network states such as chimeras. However, there are many instances when this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also
more » ... ises in the dynamical complexity of the attractors that can robustly appear - for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.
doi:10.1186/s13408-015-0033-6 pmid:26739133 pmcid:PMC4703605 fatcat:m2sisazz2ndqvb76b23kivib7m