{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T12:40:33Z","timestamp":1726317633783},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11772291"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic research Project of Universities in Henan Province","award":["21zx009"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,3,30]]},"abstract":" Turing instability is a prominent feature of reaction\u2013diffusion systems, which is widely investigated in many fields, such as ecology, neurobiology, chemistry. However, although the inhomogeneous diffusion between prey and predators exist in their network space, there are few considerations on how network diffusion affects the stability of prey\u2013predator models. Therefore, in this paper we study the pattern dynamics of a modified reaction\u2013diffusion Holling\u2013Tanner prey\u2013predator model over a random network. Specifically, we study the relationship between the node degrees of the random network and the eigenvalues of the network Laplacian matrix. Then, we obtain conditions under which the network system instability, Hopf bifurcation as well as Turing bifurcation occur. Also, we find an approximate Turing instability region of the diffusion coefficient and the connection probability of the network. Finally, we apply the mean-field approximation theory with numerical simulation to confirm the correctness of our results. The instability region indicates the random migration of the prey and predators among different communities. <\/jats:p>","DOI":"10.1142\/s0218127422500493","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T09:37:34Z","timestamp":1648719454000},"source":"Crossref","is-referenced-by-count":3,"title":["Turing Instability of a Modified Reaction\u2013Diffusion Holling\u2013Tanner Model Over a Random Network"],"prefix":"10.1142","volume":"32","author":[{"given":"Qing","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, P. R. China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-1289-8674","authenticated-orcid":false,"given":"Jianwei","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"S0218127422500493BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2003.11.004"},{"key":"S0218127422500493BIB002","first-page":"1069","volume":"16","author":"Aziz-Alaoui M. A.","year":"2003","journal-title":"Appl. Math."},{"key":"S0218127422500493BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2011.12.005"},{"key":"S0218127422500493BIB004","first-page":"897","volume":"15","author":"Camara B. I.","year":"2008","journal-title":"Dyn. Contin. Discr. Impuls. Syst. Ser. A Math. Anal."},{"key":"S0218127422500493BIB005","first-page":"1","volume":"16","author":"Camara B. I.","year":"2009","journal-title":"Dyn. Contin. Discr. Impuls. Syst."},{"key":"S0218127422500493BIB006","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ab3078"},{"key":"S0218127422500493BIB007","volume":"8","author":"Fan H.","year":"2020","journal-title":"Nat. Sci. Rev."},{"key":"S0218127422500493BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.056203"},{"key":"S0218127422500493BIB009","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-016-0028-x","volume":"7","author":"Hata S.","year":"2017","journal-title":"Sci. Rep."},{"key":"S0218127422500493BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139993253201"},{"key":"S0218127422500493BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s002850000048"},{"key":"S0218127422500493BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.05.039"},{"key":"S0218127422500493BIB013","doi-asserted-by":"publisher","DOI":"10.1038\/srep10840"},{"key":"S0218127422500493BIB014","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/35.3-4.213"},{"key":"S0218127422500493BIB015","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/47.3-4.219"},{"key":"S0218127422500493BIB016","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/hxr050"},{"key":"S0218127422500493BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-019-05460-1"},{"key":"S0218127422500493BIB018","volume-title":"A Survey of Matrix Theory and Matrix Inequalities","author":"Marcus M.","year":"1964"},{"key":"S0218127422500493BIB019","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1651"},{"key":"S0218127422500493BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2005.10.003"},{"key":"S0218127422500493BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/0022-5193(71)90154-8"},{"key":"S0218127422500493BIB022","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500003814"},{"key":"S0218127422500493BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.03.072"},{"key":"S0218127422500493BIB024","doi-asserted-by":"publisher","DOI":"10.2307\/1936296"},{"key":"S0218127422500493BIB025","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1952.0012"},{"key":"S0218127422500493BIB026","first-page":"1","volume":"5560","author":"Wang W.","year":"2012","journal-title":"Dis. Dyn. Nat. Soc."},{"key":"S0218127422500493BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.07.071"},{"key":"S0218127422500493BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2020.125304"},{"key":"S0218127422500493BIB029","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.062215"},{"key":"S0218127422500493BIB030","first-page":"1","volume":"2020","author":"Zheng Q.","year":"2020","journal-title":"Neural Plasticity"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127422500493","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T09:40:22Z","timestamp":1648719622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127422500493"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,30]]},"references-count":30,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2022,3,30]]}},"alternative-id":["10.1142\/S0218127422500493"],"URL":"https:\/\/doi.org\/10.1142\/s0218127422500493","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,30]]}}}