{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T02:20:49Z","timestamp":1776910849717,"version":"3.51.2"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T00:00:00Z","timestamp":1680652800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T00:00:00Z","timestamp":1680652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771407"],"award-info":[{"award-number":["11771407"]}],"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":["52071298"],"award-info":[{"award-number":["52071298"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010031","name":"Postdoctoral Research Foundation of China","doi-asserted-by":"publisher","award":["2022M712903"],"award-info":[{"award-number":["2022M712903"]}],"id":[{"id":"10.13039\/501100010031","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s00332-023-09907-z","type":"journal-article","created":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T15:47:52Z","timestamp":1680709672000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Nilpotent Singularities and Periodic Perturbation of a $$GI\\beta $$ Model: A Pathway to Glucose Disorder"],"prefix":"10.1007","volume":"33","author":[{"given":"Yiwen","family":"Tao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yutong","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaiping","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangnan","family":"Lyu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5392-291X","authenticated-orcid":false,"given":"Jingli","family":"Ren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,5]]},"reference":[{"issue":"2","key":"9907_CR1","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1210\/en.2015-1376","volume":"157","author":"H Ando","year":"2016","unstructured":"Ando, H., Ushijima, K., Shimba, S., et al.: Daily fasting blood glucose rhythm in male mice: a role of the circadian clock in the liver. Endocrinology 157(2), 463\u2013469 (2016)","journal-title":"Endocrinology"},{"issue":"9","key":"9907_CR2","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1111\/dme.12966","volume":"33","author":"A Aulinas","year":"2016","unstructured":"Aulinas, A., Colom, C., Patterson, A.G., et al.: Smoking affects the oral glucose tolerance test profile and the relationship between glucose and HbA1c in gestational diabetes mellitus. Diabetic Med. 33(9), 1240\u20131244 (2016)","journal-title":"Diabetic Med."},{"issue":"19","key":"9907_CR3","doi-asserted-by":"crossref","first-page":"E682","DOI":"10.1503\/cmaj.160839","volume":"189","author":"GL Booth","year":"2017","unstructured":"Booth, G.L., Luo, J., Park, A.L., et al.: Influence of environmental temperature on risk of gestational diabetes. CMAJ 189(19), E682\u2013E689 (2017)","journal-title":"CMAJ"},{"issue":"1","key":"9907_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-017-02074-2","volume":"8","author":"X Brenachot","year":"2017","unstructured":"Brenachot, X., Ramadori, G., Ioris, R.M., et al.: Hepatic protein tyrosine phosphatase receptor gamma links obesity-induced inflammation to insulin resistance. Nat. Commun. 8(1), 1\u20139 (2017)","journal-title":"Nat. Commun."},{"issue":"5","key":"9907_CR5","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.2337\/db08-0063","volume":"57","author":"A Ceriello","year":"2008","unstructured":"Ceriello, A., Esposito, K., Piconi, L., et al.: Oscillating glucose is more deleterious to endothelial function and oxidative stress than mean glucose in normal and type 2 diabetic patients. Diabetes 57(5), 1349\u20131354 (2008)","journal-title":"Diabetes"},{"issue":"11","key":"9907_CR6","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1038\/laban1109-364","volume":"38","author":"G Chakraborty","year":"2009","unstructured":"Chakraborty, G., Thumpayil, S., Lafontant, D.E., et al.: Age dependence of glucose tolerance in adult KK-Ay mice, a model of non-insulin dependent diabetes mellitus. Lab Anim. 38(11), 364\u2013368 (2009)","journal-title":"Lab Anim."},{"issue":"1","key":"9907_CR7","first-page":"1","volume":"2","author":"L Chen","year":"2012","unstructured":"Chen, L., Liu, R., Liu, Z., et al.: Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Sci. Rep. 2(1), 1\u20138 (2012)","journal-title":"Sci. Rep."},{"issue":"6","key":"9907_CR8","doi-asserted-by":"crossref","first-page":"E1462","DOI":"10.1152\/ajpendo.90444.2008","volume":"295","author":"A De Gaetano","year":"2008","unstructured":"De Gaetano, A., Hardy, T., Beck, B., et al.: Mathematical models of diabetes progression. Am. J. Physiol. Endocrinol. Metab. 295(6), E1462\u2013E1479 (2008)","journal-title":"Am. J. Physiol. Endocrinol. Metab."},{"issue":"23","key":"9907_CR9","doi-asserted-by":"crossref","first-page":"E5390","DOI":"10.1073\/pnas.1714813115","volume":"115","author":"CM Depner","year":"2018","unstructured":"Depner, C.M., Melanson, E.L., McHill, A.W., et al.: Mistimed food intake and sleep alters 24-hour time-of-day patterns of the human plasma proteome. Proc. Natl. Acad. Sci. USA 115(23), E5390\u2013E5399 (2018)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"1","key":"9907_CR10","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1093\/bioinformatics\/bts635","volume":"29","author":"A Dobin","year":"2013","unstructured":"Dobin, A., Davis, C.A., Schlesinger, F., et al.: STAR: ultrafast universal RNA-seq aligner. Bioinformatics 29(1), 15\u201321 (2013)","journal-title":"Bioinformatics"},{"issue":"7","key":"9907_CR11","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1038\/bjc.2016.37","volume":"114","author":"C Garc\u00eda-Jim\u00e9nez","year":"2016","unstructured":"Garc\u00eda-Jim\u00e9nez, C., Guti\u00e9rrez-Salmer\u00f3n, M., Chocarro-Calvo, A., et al.: From obesity to diabetes and cancer: epidemiological links and role of therapies. Br. J. Cancer 114(7), 716 (2016)","journal-title":"Br. J. Cancer"},{"issue":"2","key":"9907_CR12","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1210\/en.2015-1564","volume":"157","author":"J Ha","year":"2016","unstructured":"Ha, J., Satin, L.S., Sherman, A.S.: A mathematical model of the pathogenesis, prevention, and reversal of type 2 diabetes. Endocrinology 157(2), 624\u2013635 (2016)","journal-title":"Endocrinology"},{"issue":"5","key":"9907_CR13","doi-asserted-by":"crossref","first-page":"1524","DOI":"10.1137\/110860306","volume":"72","author":"M Huang","year":"2012","unstructured":"Huang, M., Li, J., Song, X., et al.: Modeling impulsive injections of insulin: towards artificial pancreas. SIAM J. Appl. Math. 72(5), 1524\u20131548 (2012)","journal-title":"SIAM J. Appl. Math."},{"issue":"10120","key":"9907_CR14","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/S0140-6736(17)33102-1","volume":"391","author":"MEJ Lean","year":"2018","unstructured":"Lean, M.E.J., Leslie, W.S., Barnes, A.C., et al.: Primary care-led weight management for remission of type 2 diabetes (DiRECT): an open-label, cluster-randomised trial. Lancet 391(10120), 541\u2013551 (2018)","journal-title":"Lancet"},{"issue":"3","key":"9907_CR15","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1016\/j.jtbi.2006.04.002","volume":"242","author":"J Li","year":"2006","unstructured":"Li, J., Kuang, Y., Mason, C.C.: Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays. J. Theor. Biol. 242(3), 722\u2013735 (2006)","journal-title":"J. Theor. Biol."},{"issue":"2","key":"9907_CR16","first-page":"785","volume":"23","author":"X Li","year":"2018","unstructured":"Li, X., Ren, J., Campbell, S.A., et al.: How seasonal forcing influences the complexity of a predator\u2013prey system. Discrete Contin. Dyn. B 23(2), 785 (2018)","journal-title":"Discrete Contin. Dyn. B"},{"issue":"10","key":"9907_CR17","doi-asserted-by":"crossref","first-page":"4799","DOI":"10.1109\/TAC.2020.3036035","volume":"66","author":"Y Liu","year":"2020","unstructured":"Liu, Y., Liu, J., Li, W.: Stabilization of highly nonlinear stochastic coupled systems via periodically intermittent control. IEEE Trans. Autom. Control 66(10), 4799\u20134806 (2020)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"6","key":"9907_CR18","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1111\/j.1464-5491.2008.02441.x","volume":"25","author":"A Mari","year":"2008","unstructured":"Mari, A., Tura, A., Pacini, G., et al.: Relationships between insulin secretion after intravenous and oral glucose administration in subjects with glucose tolerance ranging from normal to overt diabetes. Diabetic Med. 25(6), 671\u2013677 (2008)","journal-title":"Diabetic Med."},{"issue":"6","key":"9907_CR19","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1002\/bbpc.19850890617","volume":"89","author":"M Markus","year":"1985","unstructured":"Markus, M., M\u00fcller, S.C., Hess, B.: Observation of entrainment, quasiperiodicity and chaos in glycolyzing yeast extracts under periodic glucose input. Ber. Bunsenges. Phys. Chem. 89(6), 651\u2013654 (1985)","journal-title":"Ber. Bunsenges. Phys. Chem."},{"issue":"9","key":"9907_CR20","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1038\/ng.2383","volume":"44","author":"Meta-Analyses of Glucose and Insulin-related traits Consortium (MAGIC) Investigators","year":"2012","unstructured":"Meta-Analyses of Glucose and Insulin-related traits Consortium (MAGIC) Investigators: Large-scale association analysis provides insights into the genetic architecture and pathophysiology of type 2 diabetes. Nat. Genet. 44(9), 981 (2012)","journal-title":"Nat. Genet."},{"issue":"9","key":"9907_CR21","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1001\/jama.2017.0947","volume":"317","author":"R Micha","year":"2017","unstructured":"Micha, R., Pe\u00f1alvo, J.L., Cudhea, F., et al.: Association between dietary factors and mortality from heart disease, stroke, and type 2 diabetes in the United States. JAMA 317(9), 912\u2013924 (2017)","journal-title":"JAMA"},{"issue":"3","key":"9907_CR22","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1210\/jc.2015-3924","volume":"101","author":"CJ Morris","year":"2016","unstructured":"Morris, C.J., Purvis, T.E., Mistretta, J., et al.: Effects of the internal circadian system and circadian misalignment on glucose tolerance in chronic shift workers. J. Clin. Endocrinol. Metab. 101(3), 1066\u20131074 (2016)","journal-title":"J. Clin. Endocrinol. Metab."},{"issue":"1","key":"9907_CR23","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s13410-016-0475-8","volume":"37","author":"S Rathee","year":"2017","unstructured":"Rathee, S.: ODE models for the management of diabetes: a review. Int. J. Diabetes Dev. C. 37(1), 4\u201315 (2017)","journal-title":"Int. J. Diabetes Dev. C."},{"issue":"12","key":"9907_CR24","doi-asserted-by":"crossref","first-page":"1650203","DOI":"10.1142\/S0218127416502035","volume":"26","author":"J Ren","year":"2016","unstructured":"Ren, J., Li, X.: Bifurcations in a seasonally forced predator-prey model with generalized Holling type iv functional response. Int. J. Bifurc. Chaos 26(12), 1650203 (2016)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"6","key":"9907_CR25","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1007\/s00332-016-9323-8","volume":"26","author":"J Ren","year":"2016","unstructured":"Ren, J., Yu, L.: Codimension-two bifurcation, chaos and control in a discrete-time information diffusion model. J. Nonlinear Sci. 26(6), 1895\u20131931 (2016)","journal-title":"J. Nonlinear Sci."},{"issue":"8","key":"9907_CR26","volume":"27","author":"J Ren","year":"2017","unstructured":"Ren, J., Yuan, Q.: Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate. Chaos 27(8), 083124 (2017)","journal-title":"Chaos"},{"issue":"5","key":"9907_CR27","doi-asserted-by":"crossref","first-page":"4339","DOI":"10.1016\/j.jde.2015.11.009","volume":"260","author":"C Shan","year":"2016","unstructured":"Shan, C., Yi, Y., Zhu, H.: Nilpotent singularities and dynamics in a SIR type of compartmental model with hospital resources. J. Differ. Equ. 260(5), 4339\u20134365 (2016)","journal-title":"J. Differ. Equ."},{"issue":"11","key":"9907_CR28","volume":"27","author":"X Shi","year":"2017","unstructured":"Shi, X., Kuang, Y., Makroglou, A., et al.: Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval. Chaos 27(11), 114324 (2017)","journal-title":"Chaos"},{"issue":"6","key":"9907_CR29","doi-asserted-by":"crossref","first-page":"1763","DOI":"10.1137\/130933137","volume":"74","author":"X Song","year":"2014","unstructured":"Song, X., Huang, M., Li, J.: Modeling impulsive insulin delivery in insulin pump with time delays. SIAM J. Appl. Math. 74(6), 1763\u20131785 (2014)","journal-title":"SIAM J. Appl. Math."},{"issue":"2","key":"9907_CR30","doi-asserted-by":"crossref","first-page":"e1002379","DOI":"10.1371\/journal.pcbi.1002379","volume":"8","author":"K Sriram","year":"2012","unstructured":"Sriram, K., Rodriguez-Fernandez, M., Doyle, F.J., III.: Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans. PLoS Comput. Biol. 8(2), e1002379 (2012)","journal-title":"PLoS Comput. Biol."},{"issue":"11","key":"9907_CR31","doi-asserted-by":"crossref","first-page":"2238","DOI":"10.1038\/s41380-018-0033-5","volume":"23","author":"MB Stein","year":"2018","unstructured":"Stein, M.B., McCarthy, M.J., Chen, C.Y., et al.: Genome-wide analysis of insomnia disorder. Mol. Psychiatry 23(11), 2238\u20132250 (2018)","journal-title":"Mol. Psychiatry"},{"issue":"4","key":"9907_CR32","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1007\/s11071-018-4506-5","volume":"94","author":"Y Tao","year":"2018","unstructured":"Tao, Y., Li, X., Ren, J.: A repeated yielding model under periodic perturbation. Nonlinear Dyn. 94(4), 2511\u20132525 (2018)","journal-title":"Nonlinear Dyn."},{"issue":"6","key":"9907_CR33","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1137\/20M1378065","volume":"81","author":"Y Tao","year":"2021","unstructured":"Tao, Y., Campbell, S.A., Poulin, F.J.: Dynamics of a diffusive nutrient-phytoplankton-zooplankton model with spatio-temporal delay. SIAM J. Appl. Math. 81(6), 2405\u20132432 (2021)","journal-title":"SIAM J. Appl. Math."},{"issue":"4","key":"9907_CR34","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1006\/jtbi.2000.2150","volume":"206","author":"B Topp","year":"2000","unstructured":"Topp, B., Promislow, K., Devries, G., et al.: A model of $$\\beta $$-cell mass, insulin, and glucose kinetics: pathways to diabetes. J. Theor. Biol. 206(4), 605\u2013619 (2000)","journal-title":"J. Theor. Biol."},{"key":"9907_CR35","volume":"350","author":"KK Tsilidis","year":"2015","unstructured":"Tsilidis, K.K., Kasimis, J.C., Lopez, D.S., et al.: Type 2 diabetes and cancer: umbrella review of meta-analyses of observational studies. BMJ 350, g7607 (2015)","journal-title":"BMJ"},{"issue":"1","key":"9907_CR36","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.mbs.2010.11.005","volume":"229","author":"GC Wake","year":"2011","unstructured":"Wake, G.C., Pleasants, A.B., Vickers, M.H., et al.: The application of a model of glucose and insulin dynamics to explain an observed effect of leptin administration in reversal of developmental programming. Math. Biosci. 229(1), 109\u2013114 (2011)","journal-title":"Math. Biosci."},{"issue":"6","key":"9907_CR37","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1111\/jdi.12834","volume":"9","author":"X Wang","year":"2018","unstructured":"Wang, X., Zhao, X., Zhou, R., et al.: Delay in glucose peak time during the oral glucose tolerance test as an indicator of insulin resistance and insulin secretion in type 2 diabetes patients. J. Diabetes Investig. 9(6), 1288\u20131295 (2018)","journal-title":"J. Diabetes Investig."},{"issue":"45","key":"9907_CR38","doi-asserted-by":"crossref","first-page":"16219","DOI":"10.1073\/pnas.1408886111","volume":"111","author":"R Zhang","year":"2014","unstructured":"Zhang, R., Lahens, N.F., Ballance, H.I., et al.: A circadian gene expression atlas in mammals: implications for biology and medicine. Proc. Natl. Acad. Sci. USA 111(45), 16219\u201316224 (2014)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"6380","key":"9907_CR39","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1126\/science.aao5774","volume":"359","author":"L Zhao","year":"2018","unstructured":"Zhao, L., Zhang, F., Ding, X., et al.: Gut bacteria selectively promoted by dietary fibers alleviate type 2 diabetes. Science 359(6380), 1151\u20131156 (2018)","journal-title":"Science"},{"issue":"10027","key":"9907_CR40","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1016\/S0140-6736(16)00618-8","volume":"387","author":"B Zhou","year":"2016","unstructured":"Zhou, B., Lu, Y., Hajifathalian, K., et al.: Worldwide trends in diabetes since 1980: a pooled analysis of 751 population-based studies with 4$$\\cdot $$ 4 million participants. Lancet 387(10027), 1513\u20131530 (2016)","journal-title":"Lancet"},{"issue":"2","key":"9907_CR41","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1137\/S0036139901397285","volume":"63","author":"H Zhu","year":"2003","unstructured":"Zhu, H., Campbell, S.A., Wolkowicz, G.S.K.: Bifurcation analysis of a predator-prey system with nonmonotonic functional response. SIAM J. Appl. Math. 63(2), 636\u2013682 (2003)","journal-title":"SIAM J. Appl. Math."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-023-09907-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-023-09907-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-023-09907-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T13:13:01Z","timestamp":1683551581000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-023-09907-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,5]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["9907"],"URL":"https:\/\/doi.org\/10.1007\/s00332-023-09907-z","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,5]]},"assertion":[{"value":"3 August 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest concerning the publication of this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"49"}}