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arXiv · 2406.17359

Classification of 3-Node Restricted Excitatory-Inhibitory Networks

Manuela Aguiar·Ana Dias·Ian Stewart
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Abstract

We classify connected 3-node restricted excitatory-inhibitory networks, extending our previous paper (`Classification of 2-node Excitatory-Inhibitory Networks', Mathematical Biosciences 373 (2024) 109205). We assume that there are two node-types and two arrow-types, excitatory and inhibitory; all excitatory arrows are identical and all inhibitory arrows are identical; and excitatory (resp. inhibitory) nodes can only output excitatory (resp. inhibitory) arrows. The classification is performed under the following two network perspectives: ODE-equivalence and minimality; and valence less or equal to 2. The results of this and the previous work constitute a first step towards analysing dynamics and bifurcations of excitatory-inhibitory networks and have potential applications to biological network models.

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Manuela Aguiar, Ana Dias, Ian Stewart. 2024-06-25. Classification of 3-Node Restricted Excitatory-Inhibitory Networks. https://arxiv.org/abs/2406.17359

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