Classification of 3-Node Restricted Excitatory-Inhibitory Networks
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arXiv
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| Format: | Preprint |
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2024
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| author | Aguiar, Manuela Dias, Ana Stewart, Ian |
| author_facet | Aguiar, Manuela Dias, Ana Stewart, Ian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_17359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of 3-Node Restricted Excitatory-Inhibitory Networks Aguiar, Manuela Dias, Ana Stewart, Ian Dynamical Systems Primary: 92C42, 37N25, 37C20, Secondary: 92B20 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. |
| title | Classification of 3-Node Restricted Excitatory-Inhibitory Networks |
| topic | Dynamical Systems Primary: 92C42, 37N25, 37C20, Secondary: 92B20 |
| url | https://arxiv.org/abs/2406.17359 |