Classification of 2-node Excitatory-Inhibitory Networks
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913254766280704 |
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| author | Aguiar, Manuela Dias, Ana Stewart, Ian |
| author_facet | Aguiar, Manuela Dias, Ana Stewart, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of 2-node Excitatory-Inhibitory Networks Aguiar, Manuela Dias, Ana Stewart, Ian Dynamical Systems Primary: 92C42, 37N25, 37C20, Secondary: 92B20 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. |
| title | Classification of 2-node Excitatory-Inhibitory Networks |
| topic | Dynamical Systems Primary: 92C42, 37N25, 37C20, Secondary: 92B20 |
| url | https://arxiv.org/abs/2403.02869 |