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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:

MATCONT
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References:

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