{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T23:17:44Z","timestamp":1775603864045,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2011,12,1]],"date-time":"2011-12-01T00:00:00Z","timestamp":1322697600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2011,12]]},"DOI":"10.1007\/s11424-011-9041-0","type":"journal-article","created":{"date-parts":[[2011,12,5]],"date-time":"2011-12-05T04:59:34Z","timestamp":1323061174000},"page":"1033-1056","source":"Crossref","is-referenced-by-count":24,"title":["Codimension-two bifurcations analysis and tracking control on a discrete epidemic model"],"prefix":"10.1007","volume":"24","author":[{"given":"Na","family":"Yi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingling","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanping","family":"LIN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,12,6]]},"reference":[{"issue":"3\u20134","key":"9041_CR1","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.physa.2003.12.035","volume":"336","author":"J. Satsuma","year":"2004","unstructured":"J. Satsuma, R. Willox, A. Ramani, et al., Extending the SIR epidemic model, Physica A, 2004, 336(3\u20134): 369\u2013375.","journal-title":"Physica A"},{"issue":"1","key":"9041_CR2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.mbs.2004.01.003","volume":"189","author":"M. E. Alexander","year":"2004","unstructured":"M. E. Alexander and S. M. Moghadas, Periodicity in an epidemic model with a generalized nonlinear incidence, Mathematical Biosciences, 2004, 189(1): 75\u201396.","journal-title":"Mathematical Biosciences"},{"issue":"3","key":"9041_CR3","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s11424-006-0393-9","volume":"19","author":"H. L. Liu","year":"2006","unstructured":"H. L. Liu, J. Y. Yu, and G. T. Zhu, Global asymptotic stable eradication for the SIV epidemic model with impulsive vaccination and infection-age, Journal of Systems Science & Complexity, 2006, 19(3): 393\u2013402.","journal-title":"Journal of Systems Science & Complexity"},{"issue":"1","key":"9041_CR4","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0025-5564(01)00065-7","volume":"173","author":"C. C. Chavez","year":"2001","unstructured":"C. C. Chavez and A. A. Yakubu, Dispersal, disease and life-history evolution, Mathematical Biosciences, 2001, 173(1): 35\u201353.","journal-title":"Mathematical Biosciences"},{"issue":"5","key":"9041_CR5","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1016\/j.cnsns.2008.06.024","volume":"14","author":"Y. F. Li","year":"2009","unstructured":"Y. F. Li and J. G. Cui, The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage, Communications in Nonlinear Science and Numerical Simulation, 2009, 14(5): 2353\u20132365.","journal-title":"Communications in Nonlinear Science and Numerical Simulation"},{"issue":"4","key":"9041_CR6","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1016\/j.apm.2008.05.017","volume":"33","author":"Z. Mukandavire","year":"2009","unstructured":"Z. Mukandavire, W. Garira, and J. M. Tchuenche, Modelling effects of public health educational campaigns on HIV\/AIDS transmission dynamics, Applied Mathematical Modelling, 2009, 33(4): 2084\u20132095.","journal-title":"Applied Mathematical Modelling"},{"issue":"1","key":"9041_CR7","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.physa.2005.08.063","volume":"364","author":"A. D\u2019Innocenzo","year":"2006","unstructured":"A. D\u2019Innocenzo, F. Paladini, and L. Renna, A numerical investigation of discrete oscillating epidemic models, Physica A, 2006, 364(1): 497\u2013512.","journal-title":"Physica A"},{"issue":"4","key":"9041_CR8","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.chaos.2005.02.032","volume":"26","author":"S. J. Gao","year":"2005","unstructured":"S. J. Gao, L. S. Chen, and L. H. Sun, Dynamic complexities in a seasonal prevention epidemic model with birth pulses, Chaos, Solitons and Fractals, 2005, 26(4): 1171\u20131181.","journal-title":"Chaos, Solitons and Fractals"},{"issue":"1","key":"9041_CR9","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.physa.2003.10.051","volume":"333","author":"A. Ramani","year":"2004","unstructured":"A. Ramani, A. S. Carstea, R. Willox, and B. Grammaticos, Oscillating epidemics: A discrete-time model, Physica A, 2004, 333(1): 278\u2013292.","journal-title":"Physica A"},{"issue":"1\u20134","key":"9041_CR10","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0378-4371(00)00210-7","volume":"284","author":"V. Mendez","year":"2000","unstructured":"V. Mendez and J. Fort, Dynamical evolution of discrete epidemic models, Physica A, 2000, 284(1\u20134): 309\u2013317.","journal-title":"Physica A"},{"issue":"2","key":"9041_CR11","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.chaos.2005.01.021","volume":"26","author":"G. Z. Zeng","year":"2005","unstructured":"G. Z. Zeng, L. S. Chen, and H. Sun, Complexity of an SIR epidemic dynamics model with impulsive vaccination control, Chaos, Solitons and Fractals, 2005, 26(2): 495\u2013505.","journal-title":"Chaos, Solitons and Fractals"},{"issue":"2","key":"9041_CR12","first-page":"275","volume":"16","author":"Y. N. Xiao","year":"2003","unstructured":"Y. N. Xiao, On an SIS epidemic model with stage structure, Journal of Systems Science & Complexity, 2003, 16(2): 275\u2013288.","journal-title":"Journal of Systems Science & Complexity"},{"issue":"3","key":"9041_CR13","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.mbs.2008.01.007","volume":"212","author":"G. Seo","year":"2008","unstructured":"G. Seo and M. Kot, A comparison of two predator prey models with Holling\u2019s type I functional response, Mathematical Biosciences, 2008, 212(3): 161\u2013179.","journal-title":"Mathematical Biosciences"},{"issue":"1","key":"9041_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.nonrwa.2007.08.027","volume":"10","author":"G. W. Luo","year":"2009","unstructured":"G. W. Luo, Y. L. Zhang, and J. H. Xie, Bifurcation sequences of vibroimpact systems near a 1:2 strong resonance point, Nonlinear Analysis: Real World Applications, 2009, 10(1): 1\u201315.","journal-title":"Nonlinear Analysis: Real World Applications"},{"issue":"4","key":"9041_CR15","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1016\/j.chaos.2006.03.107","volume":"34","author":"E. Kaslik","year":"2007","unstructured":"E. Kaslik and St. Balint, Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network, Chaos, Solitons and Fractals, 2007, 34(4): 1245\u20131253.","journal-title":"Chaos, Solitons and Fractals"},{"issue":"2","key":"9041_CR16","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S1007-5704(03)00104-7","volume":"10","author":"A. Algaba","year":"2005","unstructured":"A. Algaba, E. Gamero, and A. J. Rodrguez, A bifurcation analysis of a simple electronic circuit, Communications in Nonlinear Science and Numerical Simulation, 2005, 10(2): 169\u2013178.","journal-title":"Communications in Nonlinear Science and Numerical Simulation"},{"issue":"2","key":"9041_CR17","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1016\/j.chaos.2008.02.040","volume":"41","author":"M. S. Peng","year":"2009","unstructured":"M. S. Peng, Z. H. Jiang, X. X. Jiang, et al., Multistability and complex dynamics in a simple discrete economic model, Chaos Solitons and Fractals, 2009, 41(2): 671\u2013687.","journal-title":"Chaos Solitons and Fractals"},{"issue":"1","key":"9041_CR18","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0022-0396(02)00089-X","volume":"188","author":"S. G. Ruan","year":"2003","unstructured":"S. G. Ruan and W. D. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, Journal of Differential Equations, 2003, 188(1): 135\u2013163.","journal-title":"Journal of Differential Equations"},{"key":"9041_CR19","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1017\/S0143385700009950","volume":"16","author":"H. Broer","year":"1996","unstructured":"H. Broer, R. Roussarie, and C. Simo, Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms, Ergodic Theory and Dynamical Systems, 1996, 16: 1147\u20131172.","journal-title":"Ergodic Theory and Dynamical Systems"},{"key":"9041_CR20","volume-title":"Elements of Applied Bifurcation Theory","author":"Y. Kuznetsov","year":"1998","unstructured":"Y. Kuznetsov, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 1998."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-011-9041-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-011-9041-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-011-9041-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T10:54:02Z","timestamp":1559386442000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-011-9041-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["9041"],"URL":"https:\/\/doi.org\/10.1007\/s11424-011-9041-0","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12]]}}}