{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T06:41:29Z","timestamp":1702363289245},"reference-count":43,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72171116","71671090","71871117"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101309"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["NP2020022"],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,12,15]]},"abstract":" To explore the process of online social network information interaction, in this paper, we analyze the dynamics of a discrete Lotka\u2013Volterra information diffusion model. Using the center manifold theorem, the conditions for transcritical bifurcation and flip bifurcation are obtained. With the help of approximation by a flow and Picard iteration, we explore the qualitative structures and stability of degenerate fixed point of the model with eigenvalues [Formula: see text]. What\u2019s interesting is that our results reveal a new and complex qualitative structure for fixed point, which are different from the previous reports and called degenerate saddle point. Additionally, the qualitative structures provide a new idea for investigation the stability of degenerate fixed point. Meanwhile, near the maximum user density, the dynamic results of degenerate fixed point indicate that if the intervention rate is greater than the inverse of the maximum user density, then the higher user density decreases, the lower user density increases when intrinsic growth rates are small (between 0 and 2). However, when the intrinsic growth rate is greater than 2, the high user density will continue to increase until it approaches the maximum user density indefinitely, while the small user density will approach 0, which provide us with new insights into information diffusion. Finally, we show the results of the model by numerical simulations, and the characteristics of information diffusion near the degenerate fixed point are predicted by theoretical analysis. <\/jats:p>","DOI":"10.1142\/s0218127422502285","type":"journal-article","created":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T07:39:10Z","timestamp":1671521950000},"source":"Crossref","is-referenced-by-count":1,"title":["Dynamics of a Discrete Lotka\u2013Volterra Information Diffusion Model"],"prefix":"10.1142","volume":"32","author":[{"given":"Mingshan","family":"Li","sequence":"first","affiliation":[{"name":"College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, P. R. China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-7368-1746","authenticated-orcid":false,"given":"Naiming","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, P. R. China"}]},{"given":"Ran","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Heilongjiang University, Harbin, Heilongjiang 150080, P. R. China"}]},{"given":"Xiaojun","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, Guangdong 524048, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2022,12,19]]},"reference":[{"key":"S0218127422502285BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2019.03.029"},{"key":"S0218127422502285BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2019.11.025"},{"key":"S0218127422502285BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411030416"},{"key":"S0218127422502285BIB004","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1007\/s13278-012-0085-5","volume":"3","author":"Babaei M.","year":"2013","journal-title":"Social Netw. Anal. Min."},{"key":"S0218127422502285BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5929-9"},{"key":"S0218127422502285BIB006","doi-asserted-by":"crossref","first-page":"1929","DOI":"10.1038\/s41467-017-01499-z","volume":"8","author":"Chami G. F.","year":"2017","journal-title":"Nature Commun."},{"key":"S0218127422502285BIB007","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639"},{"key":"S0218127422502285BIB008","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1145\/502512.502525","volume-title":"Proc. Seventh ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining","author":"Domingos P.","year":"2001"},{"key":"S0218127422502285BIB009","series-title":"Universitext","volume-title":"Qualitative Theory of Planar Differential Systems","author":"Dumortier F.","year":"2006"},{"key":"S0218127422502285BIB010","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2011.559468"},{"key":"S0218127422502285BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2019.05.047"},{"key":"S0218127422502285BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"S0218127422502285BIB013","first-page":"189","volume-title":"Proc. 17th Int. Conf. World Wide Web","author":"Hartline J.","year":"2008"},{"key":"S0218127422502285BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2020.124136"},{"key":"S0218127422502285BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2021.04.005"},{"key":"S0218127422502285BIB016","first-page":"665","volume":"5","author":"Jalili M.","year":"2017","journal-title":"J. Compl. Netw."},{"key":"S0218127422502285BIB017","doi-asserted-by":"crossref","first-page":"3010","DOI":"10.1038\/s41467-018-05416-w","volume":"9","author":"Jiang L.","year":"2018","journal-title":"Nature Commun."},{"key":"S0218127422502285BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3978-7"},{"key":"S0218127422502285BIB019","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010576"},{"key":"S0218127422502285BIB020","doi-asserted-by":"publisher","DOI":"10.1145\/1232722.1232727"},{"key":"S0218127422502285BIB021","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1186\/s13662-015-0655-8","volume":"2015","author":"Li C.","year":"2015","journal-title":"Adv. Diff. Eqs."},{"key":"S0218127422502285BIB022","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1186\/s13662-020-03033-w","volume":"2020","author":"Li M.-S.","year":"2020","journal-title":"Adv. Diff. Eqs."},{"key":"S0218127422502285BIB023","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1140\/epjb\/e2015-60263-6","volume":"88","author":"Lim S.","year":"2015","journal-title":"The European Phys. J. B"},{"key":"S0218127422502285BIB024","doi-asserted-by":"crossref","first-page":"20220043","DOI":"10.1098\/rsif.2022.0043","volume":"19","author":"Majhi S.","year":"2022","journal-title":"J. Roy. Soc. Interf."},{"key":"S0218127422502285BIB025","first-page":"9","volume":"261","author":"May R. M.","year":"1976","journal-title":"Nature"},{"key":"S0218127422502285BIB026","doi-asserted-by":"crossref","first-page":"2351","DOI":"10.1140\/epjst\/e2019-900201-4","volume":"228","author":"Perc M.","year":"2019","journal-title":"The Europ. Phys. J. Special Topics"},{"key":"S0218127422502285BIB027","doi-asserted-by":"crossref","first-page":"11872","DOI":"10.1038\/s41598-018-29733-8","volume":"8","author":"Qi J.","year":"2018","journal-title":"Scient. Rep."},{"key":"S0218127422502285BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-016-9323-8"},{"key":"S0218127422502285BIB029","first-page":"1843","volume":"24","author":"Ren J.","year":"2019","journal-title":"Discr. Contin. Dyn. Syst. Series B"},{"key":"S0218127422502285BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110365"},{"key":"S0218127422502285BIB031","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1137\/100793098","volume":"33","author":"Shakourifar M.","year":"2011","journal-title":"SIAM J. Scient. Comput."},{"key":"S0218127422502285BIB032","doi-asserted-by":"publisher","DOI":"10.1145\/953460.953514"},{"key":"S0218127422502285BIB033","doi-asserted-by":"publisher","DOI":"10.1038\/s41562-019-0605-7"},{"key":"S0218127422502285BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2021.125907"},{"key":"S0218127422502285BIB035","series-title":"Texts in Applied Mathematics","volume-title":"Introduction to Applied Nonlinear Dynamical Systems and Chaos","volume":"2","author":"Wiggins S.","year":"2003"},{"key":"S0218127422502285BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9919-8"},{"key":"S0218127422502285BIB037","doi-asserted-by":"crossref","first-page":"116859","DOI":"10.1016\/j.eswa.2022.116859","volume":"199","author":"Xu C.","year":"2022","journal-title":"Exp. Syst. Appl."},{"key":"S0218127422502285BIB038","author":"Xu C.","year":"2022","journal-title":"Math. Meth. Appl. Sci."},{"key":"S0218127422502285BIB039","author":"Xu C.","year":"2022","journal-title":"Math. Meth. Appl. Sci."},{"key":"S0218127422502285BIB040","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2019.1581181"},{"key":"S0218127422502285BIB041","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2017.1411909"},{"key":"S0218127422502285BIB042","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2021.1944124"},{"key":"S0218127422502285BIB043","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1038\/s41562-020-00945-1","volume":"4","author":"Zhou B.","year":"2020","journal-title":"Nature Human Behav."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127422502285","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T07:41:50Z","timestamp":1671522110000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127422502285"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,15]]},"references-count":43,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2022,12,15]]}},"alternative-id":["10.1142\/S0218127422502285"],"URL":"https:\/\/doi.org\/10.1142\/s0218127422502285","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,15]]}}}