Abstract
Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of θ-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.
Original language | English |
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Article number | 012313 |
Journal | Physical Review E |
Volume | 99 |
Issue number | 1 |
DOIs | |
Publication status | Published - 7 Jan 2019 |
Externally published | Yes |
Funding
D.A. was supported by the Engineering and Physical Sciences Research Council under Grant No. EP/P510993/1. S.C. was supported by the European Commission through the FP7 Marie Curie Initial Training Network 289146, NETT: Neural Engineering Transformative Technologies. APPENDIX A:
Funders | Funder number |
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Seventh Framework Programme | 289146 |
Engineering and Physical Sciences Research Council | EP/P510993/1 |
European Commission | |
Seventh Framework Programme |