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arXiv · 2403.02869

Classification of 2-node Excitatory-Inhibitory Networks

Manuela Aguiar·Ana Dias·Ian Stewart
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Abstract

We classify connected 2-node excitatory-inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different types of excitatory-inhibitory networks: restricted, partially restricted, unrestricted and completely unrestricted. For each type we give two different classifications. Using results on ODE-equivalence and minimality, we classify the ODE-classes and present a minimal representative for each ODE-class. We also classify all the networks with valence $\le 2$. These classifications are up to renumbering of nodes and the interchange of `excitatory' and `inhibitory' on nodes and arrows.These classifications constitute a first step towards analysing dynamics and bifurcations of excitatory-inhibitory networks. The results have potential applications to biological network models, especially neuronal networks, gene regulatory networks, and synthetic gene networks.

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BibTeXRIS

Manuela Aguiar, Ana Dias, Ian Stewart. 2024-03-05. Classification of 2-node Excitatory-Inhibitory Networks. https://arxiv.org/abs/2403.02869

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