{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T08:01:46Z","timestamp":1767772906094,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T00:00:00Z","timestamp":1562198400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T00:00:00Z","timestamp":1562198400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004681","name":"Higher Education Commission, Pakistan","doi-asserted-by":"publisher","award":["5863\/Federal\/NRPU\/R&D\/HEC\/2016"],"award-info":[{"award-number":["5863\/Federal\/NRPU\/R&D\/HEC\/2016"]}],"id":[{"id":"10.13039\/501100004681","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s00500-019-04197-8","type":"journal-article","created":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T14:09:23Z","timestamp":1562249363000},"page":"4333-4341","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Hopf bifurcation of forced Chen system and its stability via adaptive control with arbitrary parameters"],"prefix":"10.1007","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4242-9916","authenticated-orcid":false,"given":"Muhammad","family":"Marwan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Memoona","family":"Mehboob","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salman","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Aqeel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,7,4]]},"reference":[{"issue":"5","key":"4197_CR1","first-page":"061022","volume":"10","author":"MP Aghababa","year":"2015","unstructured":"Aghababa MP, Hashtarkhani B (2015) Adaptive control for fractional-order-micro-electro-mechanical resonator with nonsymmetric dead-zone input. J Comput Nonlin Dyn 10(5):061022","journal-title":"J Comput Nonlin Dyn"},{"issue":"17","key":"4197_CR2","doi-asserted-by":"crossref","first-page":"3653","DOI":"10.1002\/mma.3306","volume":"38","author":"P Balasubramaniam","year":"2015","unstructured":"Balasubramaniam P, Prakash M, Tamilalagan P (2015) Stability and hopf bifurcation analysis of immune response delayed HIV type 1 infection model with two target cells. Math Methods Appl Sci 38(17):3653\u20133669","journal-title":"Math Methods Appl Sci"},{"issue":"2","key":"4197_CR3","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.chaos.2006.09.051","volume":"37","author":"J-F Chang","year":"2006","unstructured":"Chang J-F (2006) Controlling chaos of the family of Rossler systems using sliding mode control. Chaos Solitons Fractals 37(2):609\u2013622","journal-title":"Chaos Solitons Fractals"},{"key":"4197_CR4","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1142\/S0218127499001024","volume":"9","author":"G Chen","year":"1999","unstructured":"Chen G (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9:1465\u20131466","journal-title":"Int J Bifurc Chaos"},{"issue":"7","key":"4197_CR5","doi-asserted-by":"crossref","first-page":"074501","DOI":"10.1115\/1.4032930","volume":"138","author":"X Ding","year":"2016","unstructured":"Ding X, Sinha A (2016) Hydropower plant frequency control via feedback linearization and sliding mode control. J Dyn Syst Meas Control 138(7):074501","journal-title":"J Dyn Syst Meas Control"},{"issue":"4","key":"4197_CR6","doi-asserted-by":"crossref","first-page":"2637","DOI":"10.1007\/s11071-011-0177-1","volume":"67","author":"H Guo","year":"2012","unstructured":"Guo H, Chen Y (2012) Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\/hypersonic flow. Nonlinear Dyn 67(4):2637\u20132649","journal-title":"Nonlinear Dyn"},{"key":"4197_CR7","first-page":"213","volume":"3","author":"JH Guoliang Cai","year":"2007","unstructured":"Guoliang Cai JH (2007) A new finance chaotic attractor. Int J Nonlin Sci 3:213\u2013220","journal-title":"Int J Nonlin Sci"},{"issue":"5","key":"4197_CR8","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1088\/1674-1056\/17\/5\/026","volume":"17","author":"LS Hua","year":"2008","unstructured":"Hua LS, Shi TJ, Qi JQ, Bo YX (2008) Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system. Chin Phys B 17(5):1691\u20131697","journal-title":"Chin Phys B"},{"key":"4197_CR9","first-page":"632","volume":"8","author":"A Idyanathan","year":"2015","unstructured":"Idyanathan A (2015) 3-Cells cellular neural network (CNN) attractor and its adaptive biological control. Int J Pharm Tech Res 8:632\u2013640","journal-title":"Int J Pharm Tech Res"},{"issue":"9","key":"4197_CR10","doi-asserted-by":"crossref","first-page":"091004","DOI":"10.1115\/1.4039468","volume":"140","author":"CB Kadu","year":"2018","unstructured":"Kadu CB, Khandekar AA, Patil CY (2018) Design of sliding mode controller with proportional integral sliding surface for robust regulation and tracking of process control systems. J Dyn Syst Meas Control 140(9):091004","journal-title":"J Dyn Syst Meas Control"},{"issue":"3","key":"4197_CR11","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1023\/A:1008323629064","volume":"18","author":"J Ko","year":"1999","unstructured":"Ko J, Strgance TW, Kurdila AJ (1999) Adaptive feedback linearization for the control of a typical wing section with structural nonlinearity. Nonlinear Dyn 18(3):289\u2013301","journal-title":"Nonlinear Dyn"},{"key":"4197_CR12","volume-title":"Elements of applied theory","author":"YA Kuznetsov","year":"1998","unstructured":"Kuznetsov YA (1998) Elements of applied theory. Springer, New York"},{"key":"4197_CR13","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1142\/S0218127403007394","volume":"13","author":"C Li","year":"2003","unstructured":"Li C, Chen G (2003) A note on hopf bifurcation in Chen\u2019s system. Int J Bifurc Chaos 13:1609\u20131615","journal-title":"Int J Bifurc Chaos"},{"key":"4197_CR14","doi-asserted-by":"crossref","first-page":"2857","DOI":"10.1007\/s11071-011-0194-0","volume":"67","author":"F Li","year":"2012","unstructured":"Li F, Jin Y (2012) Hopf bifurcation analysis and numerical simulation in a 4d-hyperchaotic system. Nonlinear Dyn 67:2857\u20132864","journal-title":"Nonlinear Dyn"},{"key":"4197_CR15","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s11071-012-0655-0","volume":"71","author":"H Li","year":"2013","unstructured":"Li H, Wang M (2013) Hopf bifurcation analysis in a Lorenz-type system. Nonlinear Dyn 71:235\u2013240","journal-title":"Nonlinear Dyn"},{"key":"4197_CR16","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s11071-010-9887-z","volume":"65","author":"X Li","year":"2011","unstructured":"Li X, Ou Q (2011) Dynamical properties and simulation of a new Lorenz-like chaotic system. Nonlinear Dyn 65:255\u2013270","journal-title":"Nonlinear Dyn"},{"key":"4197_CR17","first-page":"2360","volume":"49","author":"XF Li","year":"2009","unstructured":"Li XF, Chu YD, Zhang JG, Chang XY (2009) Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor. Chaos Solitons Fractals 49:2360\u20132370","journal-title":"Chaos Solitons Fractals"},{"key":"4197_CR18","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1016\/j.chaos.2004.02.060","volume":"22","author":"CX Liu","year":"2004","unstructured":"Liu CX (2004) A new chaotic attractor. Chaos Solitons Fractals 22:1031\u20131038","journal-title":"Chaos Solitons Fractals"},{"key":"4197_CR19","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/S0375-9601(01)00383-8","volume":"286","author":"J Lu","year":"2001","unstructured":"Lu J, Zhang S (2001) Controlling Chen\u2019s chaotic attractor using backstepping design based on parameters identification. Int J Phys Lett A 286:148\u2013152","journal-title":"Int J Phys Lett A"},{"key":"4197_CR20","doi-asserted-by":"crossref","first-page":"2257","DOI":"10.1142\/S0218127402005819","volume":"12","author":"J Lu","year":"2002","unstructured":"Lu J, Zhou T, Chen G, Zhang S (2002) Local bifurcations of the Chen system. Int J Bifurc Chaos 12:2257\u20132270","journal-title":"Int J Bifurc Chaos"},{"key":"4197_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6374-6","volume-title":"The Hopf bifurcation and its applications","author":"JE Marsden","year":"1976","unstructured":"Marsden JE, McCracken M (1976) The Hopf bifurcation and its applications. Springer, Berlin"},{"issue":"4","key":"4197_CR22","doi-asserted-by":"crossref","first-page":"041010","DOI":"10.1115\/1.4042030","volume":"141","author":"M Marwan","year":"2018","unstructured":"Marwan M, Ahmad S, Aqeel M, Sabir M (2018) Control analysis of Rucklidge chaotic system. J Dyn Syst Meas Control 141(4):041010","journal-title":"J Dyn Syst Meas Control"},{"key":"4197_CR23","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/j.chaos.2006.01.071","volume":"33","author":"JM Nazzal","year":"2007","unstructured":"Nazzal JM, Natsheh AN (2007) Chaos control using sliding-mode theory. Chaos Solitons Fractals 33:695\u2013702","journal-title":"Chaos Solitons Fractals"},{"key":"4197_CR24","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/0375-9601(76)90101-8","volume":"57","author":"R Oe","year":"1976","unstructured":"Oe R (1976) An equation for continuous chaos. Phys Lett A 57:397\u2013398","journal-title":"Phys Lett A"},{"key":"4197_CR25","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1103\/PhysRevLett.65.349","volume":"65","author":"E Ott","year":"1990","unstructured":"Ott E, Grebogi C, Yorke J (1990) Using chaos to direct trajectories to targets. Phys Rev Lett 65:349\u2013354","journal-title":"Phys Rev Lett"},{"issue":"9","key":"4197_CR26","doi-asserted-by":"crossref","first-page":"091006","DOI":"10.1115\/1.4039483","volume":"140","author":"AK Patra","year":"2018","unstructured":"Patra AK, Rout PK (2018) Backstepping sliding mode Gaussian insulin injection control for blood glucose regulation in type I diabetes patient. J Dyn Syst Meas Control 140(9):091006","journal-title":"J Dyn Syst Meas Control"},{"key":"4197_CR27","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/j.chaos.2006.09.057","volume":"37","author":"CC Peng","year":"2008","unstructured":"Peng CC, Chen CL (2008) Robust chaotic control of Lorenz system by backstepping design. Chaos Solitons Fractals 37:598\u2013608","journal-title":"Chaos Solitons Fractals"},{"issue":"05","key":"4197_CR28","doi-asserted-by":"crossref","first-page":"1550059","DOI":"10.1142\/S179352451550059X","volume":"8","author":"M Prakash","year":"2015","unstructured":"Prakash M, Balasubramaniam P (2015) Stability and multi-parametric hopf bifurcation analyses of viral infection model with time delay. Int J Biomath 8(05):1550059","journal-title":"Int J Biomath"},{"key":"4197_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cnsns.2015.10.012","volume":"35","author":"M Prakash","year":"2016","unstructured":"Prakash M, Balasubramaniam P (2016a) Bifurcation analysis of macrophages infection model with delayed immune response. Commun Nonlin Sci Numer Simul 35:1\u201316","journal-title":"Commun Nonlin Sci Numer Simul"},{"issue":"6","key":"4197_CR30","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1002\/cplx.21678","volume":"21","author":"M Prakash","year":"2016","unstructured":"Prakash M, Balasubramaniam P (2016b) Stability and hopf bifurcation analysis of novel hyperchaotic system with delayed feedback control. Complexity 21(6):180\u2013193","journal-title":"Complexity"},{"issue":"5","key":"4197_CR31","doi-asserted-by":"crossref","first-page":"051001","DOI":"10.1115\/1.4039189","volume":"13","author":"B Quan","year":"2018","unstructured":"Quan B, Wang C, Sun J, Zhao Y (2018) A novel adaptive control projective synchronization of chaotic systems. J Comput Nonlinear Dyn 13(5):051001","journal-title":"J Comput Nonlinear Dyn"},{"key":"4197_CR32","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1017\/S0022112092003392","volume":"237","author":"AM Rucklidge","year":"1992","unstructured":"Rucklidge AM (1992) Chaos in models of double convection. J Fluid Mech 237:209\u2013229","journal-title":"J Fluid Mech"},{"key":"4197_CR33","first-page":"158","volume":"1522","author":"LT Soon","year":"2013","unstructured":"Soon LT, Salleh Z (2013) Hopf bifurcation analysis of a modified Lorenz system. AIP Conf Proc 1522:158\u2013168","journal-title":"AIP Conf Proc"},{"key":"4197_CR34","volume-title":"Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering","author":"SH Strogatz","year":"2014","unstructured":"Strogatz SH (2014) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Westview Press, Boulder"},{"issue":"2","key":"4197_CR35","first-page":"18","volume":"4","author":"V Sundarpandian","year":"2011","unstructured":"Sundarpandian V, Karthikeyan R (2011) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen system by adaptive control. Int J Syst Signal Control Eng Appl 4(2):18\u201325","journal-title":"Int J Syst Signal Control Eng Appl"},{"key":"4197_CR36","unstructured":"Tang JS, Xiao H (2007) Amplitude control of limit cycle of coupled Vander pol oscillator. Acta Phys Sin 56(1):101\u2013105"},{"issue":"6","key":"4197_CR37","doi-asserted-by":"crossref","first-page":"061022","DOI":"10.1115\/1.4029604","volume":"10","author":"X Tian","year":"2015","unstructured":"Tian X, Feii S (2015) Adaptive control for fractional-order-micro-electro-mechanical resonator with nonsymmetric dead-zone input. J Comput Nonlin Dyn 10(6):061022","journal-title":"J Comput Nonlin Dyn"},{"key":"4197_CR38","first-page":"632","volume":"8","author":"S Vaidyanathan","year":"2015","unstructured":"Vaidyanathan S (2015) 3-cells cellular neural network (cnn) attractor and its adaptive biological control. Int J Pharm Tech Res 8:632\u2013640","journal-title":"Int J Pharm Tech Res"},{"key":"4197_CR39","volume-title":"Introduction to applied nonlinear dynamical system and chaos","author":"S Wiggins","year":"2003","unstructured":"Wiggins S (2003) Introduction to applied nonlinear dynamical system and chaos. Springer, New York"},{"issue":"3","key":"4197_CR40","doi-asserted-by":"crossref","first-page":"031012","DOI":"10.1115\/1.4027683","volume":"10","author":"X Wu","year":"2015","unstructured":"Wu X, Chi M (2015) Parameters study of hopf bifurcation in railway vehicle system. J Comput Nonlin Dyn 10(3):031012","journal-title":"J Comput Nonlin Dyn"},{"key":"4197_CR41","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1016\/S0960-0779(02)00659-8","volume":"18","author":"W Xiao-Qun","year":"2003","unstructured":"Xiao-Qun W, Jun-An L (2003) Parametric identification and backstepping control of uncertain l$$\\ddot{u}$$ system. Chaos Solitons Fractals 18:721\u2013729","journal-title":"Chaos Solitons Fractals"},{"key":"4197_CR42","first-page":"1410","volume":"14","author":"T Yang","year":"2009","unstructured":"Yang T (2009) A detailed study of adaptive control of chaotic systems with unknown parameters. Int J Dyn Control 14:1410\u20131417","journal-title":"Int J Dyn Control"},{"issue":"1","key":"4197_CR43","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1515\/dema-2013-0426","volume":"46","author":"MT Yassen","year":"2013","unstructured":"Yassen MT, El-Dessoky MM, Saleh E, Aly ES (2013) On hopf bifurcation of Liu chaotic system. Demonstr Math 46(1):111\u2013122","journal-title":"Demonstr Math"},{"key":"4197_CR44","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.chaos.2004.02.004","volume":"22","author":"HT Yau","year":"2004","unstructured":"Yau HT (2004) Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals 22:341\u2013347","journal-title":"Chaos Solitons Fractals"},{"key":"4197_CR45","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1016\/S0960-0779(02)00205-9","volume":"15","author":"Y Yongguang","year":"2003","unstructured":"Yongguang Y, Suochun Z (2003) Controlling uncertain l$$\\ddot{u}$$ using backstepping design. Chaos Solitons Fractals 15:897\u2013902","journal-title":"Chaos Solitons Fractals"},{"issue":"2","key":"4197_CR46","first-page":"014501","volume":"9","author":"Z Zhang","year":"2014","unstructured":"Zhang Z, Yang H (2014) Hopf bifurcation analysis for a novel hyperchaotic system. J Comput Nonlin Dyn 9(2):014501","journal-title":"J Comput Nonlin Dyn"},{"issue":"1","key":"4197_CR47","doi-asserted-by":"crossref","first-page":"014501","DOI":"10.1115\/1.4006327","volume":"8","author":"K Zhuang","year":"2012","unstructured":"Zhuang K (2012) Hopf bifurcation analysis for a novel hyperchaotic system. J Comput Nonlin Dyn 8(1):014501","journal-title":"J Comput Nonlin Dyn"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-019-04197-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-019-04197-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-019-04197-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,20]],"date-time":"2024-07-20T16:35:38Z","timestamp":1721493338000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-019-04197-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,4]]},"references-count":47,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["4197"],"URL":"https:\/\/doi.org\/10.1007\/s00500-019-04197-8","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2019,7,4]]},"assertion":[{"value":"4 July 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"All authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the author.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}