Abstract
We investigate the clustering dynamics of a network of inhibitory interneurons, where each neuron is connected to some set of its neighbors. We use phase model analysis to study the existence and stability of cluster solutions. In particular, we describe cluster solutions which exist for any type of oscillator, coupling and connectivity. We derive conditions for the stability of these solutions in the case where each neuron is coupled to its two nearest neighbors on each side. We apply our analysis to show that changing the connection weights in the network can change the stability of solutions in the inhibitory network. Numerical simulations of the full network model confirm and supplement our theoretical analysis. Our results support the hypothesis that cluster solutions may be related to the formation of neural assemblies.
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Acknowledgements
The work described in this chapter is a result of a collaboration made possible by the IMA’s workshop, WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Dynamical Systems with Applications to Biology and Medicine.
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Miller, J., Ryu, H., Teymuroglu, Z., Wang, X., Booth, V., Campbell, S.A. (2015). Clustering in Inhibitory Neural Networks with Nearest Neighbor Coupling. In: Jackson, T., Radunskaya, A. (eds) Applications of Dynamical Systems in Biology and Medicine. The IMA Volumes in Mathematics and its Applications, vol 158. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2782-1_5
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DOI: https://doi.org/10.1007/978-1-4939-2782-1_5
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