{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:51:42Z","timestamp":1776811902766,"version":"3.51.2"},"reference-count":26,"publisher":"European Society of Computational Methods in Sciences and Engineering","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"published-print":{"date-parts":[[2018,2,22]]},"DOI":"10.3233\/jcm-170773","type":"journal-article","created":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T12:35:38Z","timestamp":1508243738000},"page":"85-115","source":"Crossref","is-referenced-by-count":3,"title":["Numerical approximation of nonhomogeneous boundary conditions on networks for a hyperbolic system of chemotaxis modeling the Physarum dynamics"],"prefix":"10.66113","volume":"18","author":[{"given":"Gabriella","family":"Bretti","sequence":"first","affiliation":[]},{"given":"Roberto","family":"Natalini","sequence":"additional","affiliation":[]}],"member":"55691","reference":[{"key":"10.3233\/JCM-170773_ref1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.jtbi.2012.06.017","article-title":"Physarum can compute the shortest path","volume":"309","author":"Bonifaci","year":"2012","journal-title":"Journal of Theoretical Biology"},{"key":"10.3233\/JCM-170773_ref2","unstructured":"S. Borsche, A. Klar and T.N.H. Pham, Kinetic and related macroscopic models for chemotaxis on networks, preprint ArXiv: 1512.07001v 1 (2015),"},{"issue":"2","key":"10.3233\/JCM-170773_ref3","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1142\/S0218202513400071","article-title":"The scalar Keller-Segel model on networks","volume":"24","author":"Borsche","year":"2014","journal-title":"Mathematical Models and Methods in Applied Sciences"},{"issue":"1","key":"10.3233\/JCM-170773_ref4","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1051\/m2an\/2013098","article-title":"A hyperbolic model of chemotaxis on a network: A numerical study","volume":"48","author":"Bretti","year":"2014","journal-title":"Mathematical Modelling and Numerical Analysis"},{"key":"10.3233\/JCM-170773_ref5","unstructured":"F. Camilli and L. Corrias, Parabolic models for chemotaxis on weighted networks, preprint ArXiv: 1511 07279 (2015)."},{"key":"10.3233\/JCM-170773_ref6","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00285-002-0173-7","article-title":"Cattaneo models for chemosensitive movement, numerical solution and pattern formation","volume":"46","author":"Dolak","year":"2003","journal-title":"J Math Biol"},{"issue":"2","key":"10.3233\/JCM-170773_ref7","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s00285-004-0286-2","article-title":"Derivation of hyperbolic models for chemosensitive movement","volume":"50","author":"Filbet","year":"2005","journal-title":"J Math Biol"},{"key":"10.3233\/JCM-170773_ref8","doi-asserted-by":"crossref","first-page":"118101.1","DOI":"10.1103\/PhysRevLett.90.118101","article-title":"Percolation, morphogenesis, and burgers dynamics in blood vessels formation","volume":"90","author":"Gamba","year":"2003","journal-title":"Phys Rev Letters"},{"issue":"2","key":"10.3233\/JCM-170773_ref10","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1016\/j.jmaa.2011.10.039","article-title":"Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes","volume":"388","author":"Gosse","year":"2012","journal-title":"J Math Anal Appl"},{"issue":"1","key":"10.3233\/JCM-170773_ref11","doi-asserted-by":"crossref","first-page":"A520","DOI":"10.1137\/10081753X","article-title":"Well-balanced numerical approximations display asymptotic decay toward Maxwellian distributions for a model of chemotaxis in a bounded interval","volume":"34","author":"Gosse","year":"2012","journal-title":"SIAM J Sci Comput"},{"key":"10.3233\/JCM-170773_ref12","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1090\/S0002-9947-1987-0871674-4","article-title":"Stability results for a diffusion equation with functional drift approximating a chemotaxis model","volume":"300","author":"Greenberg","year":"1987","journal-title":"Trans Amer Math Soc"},{"key":"10.3233\/JCM-170773_ref13","doi-asserted-by":"crossref","first-page":"39","DOI":"10.3934\/dcdsb.2009.12.39","article-title":"Stability of constant states and qualitative behavior of solutions to a one dimensional hyperbolic model of chemotaxis","volume":"12","author":"Guarguaglini","year":"2009","journal-title":"Discrete Contin Dyn Syst Ser B"},{"key":"10.3233\/JCM-170773_ref14","unstructured":"F.R. Guarguaglini and R. Natalini, Global smooth solutions for a hyperbolic chemotaxis model on a network, SIAM J Math Anal, in press."},{"key":"10.3233\/JCM-170773_ref15","first-page":"103","article-title":"From 1970 until present: The Keller-Segel model in chemotaxis and its consequences","volume":"105","author":"Horstmann","year":"2003","journal-title":"Jahresber Deutsch Math-Verein"},{"key":"10.3233\/JCM-170773_ref16","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0022-5193(70)90092-5","article-title":"Initiation of slime mold aggregation viewed as an instability","volume":"26","author":"Keller","year":"1970","journal-title":"J Theor Biol"},{"key":"10.3233\/JCM-170773_ref17","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0006-3002(58)90330-5","article-title":"Thermodynamic analysis of the permeability of biological membrane to non-electrolytes","volume":"27","author":"Kedem","year":"1958","journal-title":"Biochimica et Biophysica Acta"},{"key":"10.3233\/JCM-170773_ref18","doi-asserted-by":"crossref","first-page":"445","DOI":"10.14492\/hokmj\/1277472812","article-title":"Mathematical analysis to an adaptive network of the plasmodium system","volume":"36","author":"Miyaji","year":"2007","journal-title":"Hokkaido Math J"},{"key":"10.3233\/JCM-170773_ref19","first-page":"353","article-title":"Physarum can solve the shortest path problem on Riemannian surface mathematically rigorously","volume":"46","author":"Miyaji","year":"2008","journal-title":"Int J Pure Appl Math"},{"key":"10.3233\/JCM-170773_ref21","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1038\/35035159","article-title":"Maze-solving by an amoeboid organism","volume":"407","author":"Nakagaki","year":"2000","journal-title":"Nature"},{"key":"10.3233\/JCM-170773_ref22","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1137\/100803067","article-title":"An asymptotic high order mass-preserving scheme for a hyperbolic model of chemotaxis","volume":"50","author":"Natalini","year":"2012","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"10.3233\/JCM-170773_ref23","doi-asserted-by":"crossref","unstructured":"B. Perthame, Transport equations in biology, Frontiers in Mathematics, Birkh\u00e4user (2007).","DOI":"10.1007\/978-3-7643-7842-4"},{"key":"10.3233\/JCM-170773_ref24","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.physd.2005.01.010","article-title":"A coupled-oscilator model with a conservation law for the rhythmic amoeboid movement of plasmodial slime molds","volume":"205","author":"Tero","year":"2005","journal-title":"Phys D"},{"key":"10.3233\/JCM-170773_ref25","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.jtbi.2006.07.015","article-title":"A mathematical model for adaptive transport network in path finding by true slime mold","volume":"244","author":"Tero","year":"2007","journal-title":"J Theoret Biol"},{"key":"10.3233\/JCM-170773_ref26","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1126\/science.1177894","article-title":"Rules for biologically inspired adaptive network design","volume":"327","author":"Tero","year":"2010","journal-title":"Science"},{"key":"10.3233\/JCM-170773_ref27","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1137\/0132054","article-title":"A theoretical study of receptor mechanisms in bacterial chemotaxis","volume":"32","author":"Segel","year":"1977","journal-title":"SIAM J Appl Math"},{"key":"10.3233\/JCM-170773_ref28","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.biosystems.2011.05.001","article-title":"Traffic optimization in railroad networks using an algorithm mimicking an amoeba-like organism, Physarum plasmodium","volume":"105","author":"Watanabe","year":"2011","journal-title":"ByoSystems"}],"container-title":["Journal of Computational Methods in Sciences and Engineering"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JCM-170773","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:07:28Z","timestamp":1776809248000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JCM-170773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,22]]},"references-count":26,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/jcm-170773","relation":{},"ISSN":["1472-7978","1875-8983"],"issn-type":[{"value":"1472-7978","type":"print"},{"value":"1875-8983","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,22]]}}}