{"title":"Classification of 2-node excitatory–inhibitory networks","authors":"Manuela Aguiar , Ana Dias , Ian Stewart","doi":"10.1016/j.mbs.2024.109205","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span><math><mrow><mo>≤</mo><mn>2</mn></mrow></math></span>. 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.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424000658/pdfft?md5=0de2d8c0f1c08de96b7441cf8d82296b&pid=1-s2.0-S0025556424000658-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Biosciences","FirstCategoryId":"99","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0025556424000658","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
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 . 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.
期刊介绍:
Mathematical Biosciences publishes work providing new concepts or new understanding of biological systems using mathematical models, or methodological articles likely to find application to multiple biological systems. Papers are expected to present a major research finding of broad significance for the biological sciences, or mathematical biology. Mathematical Biosciences welcomes original research articles, letters, reviews and perspectives.