{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:41:46Z","timestamp":1772296906571,"version":"3.50.1"},"reference-count":48,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371112"],"award-info":[{"award-number":["11371112"]}],"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":["11031002"],"award-info":[{"award-number":["11031002"]}],"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":["A201208"],"award-info":[{"award-number":["A201208"]}],"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":["11371112"],"award-info":[{"award-number":["11371112"]}],"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":["11031002"],"award-info":[{"award-number":["11031002"]}],"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":["A201208"],"award-info":[{"award-number":["A201208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Heilongjiang Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["11371112"],"award-info":[{"award-number":["11371112"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100005046","name":"Heilongjiang Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["11031002"],"award-info":[{"award-number":["11031002"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100005046","name":"Heilongjiang Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["A201208"],"award-info":[{"award-number":["A201208"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stable periodic orbits. By the normal form and center manifold theory, the direction of the Hopf bifurcation and stability of the bifurcating periodic orbits are determined. Numerical simulations are provided to support our theoretical conclusions.<\/jats:p>","DOI":"10.1155\/2014\/929580","type":"journal-article","created":{"date-parts":[[2014,2,26]],"date-time":"2014-02-26T06:14:41Z","timestamp":1393395281000},"page":"1-10","source":"Crossref","is-referenced-by-count":7,"title":["Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay"],"prefix":"10.1155","volume":"2014","author":[{"given":"Haitao","family":"Song","sequence":"first","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiaochu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Architecture, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weihua","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","year":"1990"},{"issue":"1","key":"2","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/0167-4048(87)90122-2","volume":"6","year":"1987","journal-title":"Computers and Security"},{"key":"3","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1098\/rspa.1933.0106","volume":"141","year":"1933","journal-title":"Proceedings of the Royal Society A"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(03)00113-0"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.03.023"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.09.062"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2005.0051"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/841987"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/260962"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2012.07.005"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s10956-008-9102-x"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.10.003"},{"key":"13","series-title":"Fields Inst. Commun.","first-page":"459","volume-title":"Global stability in cyclic epidemic models with disease fatalities","volume":"21","year":"1999"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.062"},{"issue":"4","key":"15","doi-asserted-by":"crossref","first-page":"448","DOI":"10.15388\/NA.17.4.14050","volume":"17","year":"2012","journal-title":"Nonlinear Analysis: Modelling and Control"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/s002850050194"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(02)00089-X"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1080\/13873950500064293"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2012.669387"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2012.9.785"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-011-9628-6"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2011.11.002"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.01.004"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2003.11.005"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1137\/120872942"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139997321219"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1137\/090779322"},{"issue":"3","key":"28","first-page":"259","volume":"14","year":"2006","journal-title":"Canadian Applied Mathematics Quarterly"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524511001490"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2010.7.675"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1137\/090780821"},{"issue":"3","key":"32","first-page":"1","volume":"2013","year":"2013","journal-title":"Electronic Journal of Qualitative Theory of Differential Equations"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2012.9.685"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00009-3"},{"issue":"6","key":"35","first-page":"863","volume":"10","year":"2003","journal-title":"Dynamics of Continuous, Discrete & Impulsive Systems. Series A"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(02)00062-6"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.03.012"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2007.01.003"},{"issue":"1","key":"39","first-page":"1","volume":"2013","year":"2013","journal-title":"Electronic Journal of Qualitative Theory of Differential Equations"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.10.048"},{"key":"41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.09.008"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.10.034"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.05.072"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.03.023"},{"key":"45","series-title":"Applied Mathematical Sciences","volume":"99","year":"1993"},{"key":"46","series-title":"London Mathematical Society Lecture Note Series","first-page":"v+311 pp. (microfiche insert)","volume":"41","year":"1981"},{"key":"47","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.11.010"},{"key":"48","series-title":"Regional Conference Series in Applied Mathematics","first-page":"v+76","year":"1976"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/929580.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/929580.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/929580.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,15]],"date-time":"2020-08-15T19:46:58Z","timestamp":1597520818000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/929580\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":48,"alternative-id":["929580","929580"],"URL":"https:\/\/doi.org\/10.1155\/2014\/929580","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}