# Bifurcations of a Neural Network Model with Symmetry

@article{Parker2022BifurcationsOA, title={Bifurcations of a Neural Network Model with Symmetry}, author={Ross Parker and Andrea K. Barreiro}, journal={SIAM Journal on Applied Dynamical Systems}, year={2022} }

. We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength g is varied. We primarily consider two network topologies: an all-to-all connected network which excludes self-connections, and a network in which the excitatory cells are broken into clusters of equal size. Although in both cases the bifurcation structure is determined by symmetries in the…

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