{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T23:52:04Z","timestamp":1780098724078,"version":"3.54.0"},"reference-count":80,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,13]],"date-time":"2018-01-13T00:00:00Z","timestamp":1515801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system) as well as in their discrete Boolean versions (e.g., non-linear Hopfield system); in both cases, the notion of interaction graph G(J) associated to its Jacobian matrix J, and also the concepts of frustrated nodes, positive or negative circuits of G(J), kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i) attractor entropy, (ii) isochronal entropy and (iii) entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.<\/jats:p>","DOI":"10.3390\/e20010036","type":"journal-article","created":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T12:30:36Z","timestamp":1516019436000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8335-9240","authenticated-orcid":false,"given":"Jacques","family":"Demongeot","sequence":"first","affiliation":[{"name":"Team AGIM (Autonomy, Gerontechnology, Imaging, Modelling &amp; Tools for e-Gnosis Medical), Laboratory AGEIS, University Grenoble Alpes, Faculty of Medicine, La Tronche 38700, France"},{"name":"Escuela de Ingenier\u00eda Civil en Inform\u00e1tica, Universidad de Valpara\u00edso, General Cruz 222, Valpara\u00edso 2340000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4786-4271","authenticated-orcid":false,"given":"Mariem","family":"Jelassi","sequence":"additional","affiliation":[{"name":"Team AGIM (Autonomy, Gerontechnology, Imaging, Modelling &amp; Tools for e-Gnosis Medical), Laboratory AGEIS, University Grenoble Alpes, Faculty of Medicine, La Tronche 38700, France"},{"name":"Laboratory of Bioinformatics, Biomathematics and Biostatistics (BIMS), Institut Pasteur de Tunis, Tunis 1002, Tunisia"},{"name":"National School for Computer Studies, RIADI Laboratory, University of Manouba, Manouba 2010, Tunisia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hana","family":"Hazgui","sequence":"additional","affiliation":[{"name":"Team AGIM (Autonomy, Gerontechnology, Imaging, Modelling &amp; Tools for e-Gnosis Medical), Laboratory AGEIS, University Grenoble Alpes, Faculty of Medicine, La Tronche 38700, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Slimane","family":"Ben Miled","sequence":"additional","affiliation":[{"name":"Laboratory of Bioinformatics, Biomathematics and Biostatistics (BIMS), Institut Pasteur de Tunis, Tunis 1002, Tunisia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Narjes","family":"Bellamine Ben Saoud","sequence":"additional","affiliation":[{"name":"National School for Computer Studies, RIADI Laboratory, University of Manouba, Manouba 2010, Tunisia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carla","family":"Taramasco","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Civil en Inform\u00e1tica, Universidad de Valpara\u00edso, General Cruz 222, Valpara\u00edso 2340000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1049\/iet-syb:20060038","article-title":"Graph theory and networks in biology","volume":"1","author":"Mason","year":"2007","journal-title":"IET Syst. 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