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**Symmetries constrain dynamics in a family of balanced neural networks.**
*(English)*
Zbl 1395.92029

Summary: We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale’s Law – each neuron makes either excitatory or inhibitory connections onto its post-synaptic targets. We find that this constrained system may be described as a perturbation from a system with nontrivial symmetries. We analyze the symmetric system using the tools of equivariant bifurcation theory and demonstrate that the symmetry-implied structures remain evident in the perturbed system. In comparison, spectral characteristics of the network coupling matrix are relatively uninformative about the behavior of the constrained system.

### MSC:

92C20 | Neural biology |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

37N25 | Dynamical systems in biology |

37G40 | Dynamical aspects of symmetries, equivariant bifurcation theory |

### Software:

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\textit{A. K. Barreiro} et al., J. Math. Neurosci. 7, Paper No. 10, 28 p. (2017; Zbl 1395.92029)

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