{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T13:26:11Z","timestamp":1751894771994},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2013,12,29]],"date-time":"2013-12-29T00:00:00Z","timestamp":1388275200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1007\/s00521-013-1539-z","type":"journal-article","created":{"date-parts":[[2013,12,28]],"date-time":"2013-12-28T03:50:04Z","timestamp":1388202604000},"page":"683-692","source":"Crossref","is-referenced-by-count":13,"title":["Chaos control of a bounded 4D chaotic system"],"prefix":"10.1007","volume":"25","author":[{"given":"Hassan","family":"Saberi Nik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahin","family":"Golchaman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,29]]},"reference":[{"key":"1539_CR1","doi-asserted-by":"crossref","DOI":"10.1142\/2637","volume-title":"Nonlinear oscillators: controlling and synchronization","author":"M Lakshmanan","year":"1996","unstructured":"Lakshmanan M, Murali K (1996) Nonlinear oscillators: controlling and synchronization. World Scientific, Singapore"},{"key":"1539_CR2","doi-asserted-by":"crossref","first-page":"3190","DOI":"10.1103\/PhysRevLett.75.3190","volume":"75","author":"SK Han","year":"1995","unstructured":"Han SK, Kerrer C, Kuramoto Y (1995) Dephasing and bursting in coupled neural oscillators. Phys Rev Lett 75:3190\u20133193","journal-title":"Phys Rev Lett"},{"key":"1539_CR3","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1038\/20676","volume":"399","author":"B Blasius","year":"1999","unstructured":"Blasius B, Huppert A, Stone L (1999) Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399:354\u2013359","journal-title":"Nature"},{"issue":"4","key":"1539_CR4","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1007\/s11071-012-0424-0","volume":"69","author":"SR Choudhury","year":"2012","unstructured":"Choudhury SR, Van Gorder RA (2012) Competitive modes as reliable predictors of chaos versus hyperchaos and as geometric mappings accurately delimiting attractors. Nonlinear Dyn 69(4):2255\u20132267","journal-title":"Nonlinear Dyn"},{"issue":"4","key":"1539_CR5","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1007\/s11071-013-0756-4","volume":"72","author":"RA Van Gorder","year":"2013","unstructured":"Van Gorder RA (2013) Shil\u2019nikov chaos in the 4D Lorenz\u2013Stenflo system modeling the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. Nonlinear Dyn 72(4):837\u2013851","journal-title":"Nonlinear Dyn"},{"key":"1539_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511803260","volume-title":"Chaos in dynamical systems","author":"E Ott","year":"2002","unstructured":"Ott E (2002) Chaos in dynamical systems, 2nd edn. Cambridge University Press, Cambridge","edition":"2"},{"key":"1539_CR7","volume-title":"Controlling chaos and bifurcation in engineering systems","author":"G Chen","year":"2000","unstructured":"Chen G (2000) Controlling chaos and bifurcation in engineering systems. CRC Press, Boca Raton"},{"issue":"3-4","key":"1539_CR8","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1007\/s00521-012-0964-8","volume":"23","author":"M Zhao","year":"2013","unstructured":"Zhao M, Zhang H, Wang Z (2013) Synchronization in complex dynamical networks based on the feedback of scalar signals. Neural Comput Appl 23(3\u20134):683\u2013689","journal-title":"Neural Comput Appl"},{"key":"1539_CR9","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1016\/j.physleta.2010.01.048","volume":"374","author":"WG Yu","year":"2010","unstructured":"Yu WG (2010) Stabilization of three-dimensional chaotic systems via single state feedback controller. Phys Lett A 374:1488\u20131492","journal-title":"Phys Lett A"},{"key":"1539_CR10","doi-asserted-by":"crossref","first-page":"3080","DOI":"10.1016\/j.apm.2010.12.020","volume":"35","author":"MP Aghababa","year":"2011","unstructured":"Aghababa MP, Khanmohammadi S, Alizadeh G (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl Math Model 35:3080\u20133091","journal-title":"Appl Math Model"},{"key":"1539_CR11","doi-asserted-by":"crossref","unstructured":"Li C, Gao DY, Liu C, Chen G (2013) Impulsive control for synchronizing delayed discrete complex networks with switching topology. Neural Comput Appl. doi: 10.1007\/s00521-013-1470-3","DOI":"10.1007\/s00521-013-1470-3"},{"key":"1539_CR12","doi-asserted-by":"crossref","first-page":"2514","DOI":"10.1016\/j.cnsns.2009.09.015","volume":"15","author":"P Wang","year":"2010","unstructured":"Wang P, Li D, Hu Q (2010) Bounds of the hyper-chaotic Lorenz\u2013Stenflo system. Commun Nonlinear Sci Numer Simul 15:2514\u20132520","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1539_CR13","doi-asserted-by":"crossref","first-page":"2679","DOI":"10.1142\/S0218127411030027","volume":"21","author":"P Wang","year":"2011","unstructured":"Wang P, Li D, Wu X, L\u00fc J, Yu X (2011) Ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems. Int J Bifurc Chaos Appl Sci Eng 21:2679\u20132694","journal-title":"Int J Bifurc Chaos Appl Sci Eng"},{"key":"1539_CR14","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.chaos.2011.01.001","volume":"44","author":"F Zhang","year":"2011","unstructured":"Zhang F, Shu Y, Yang H, Li X (2011) Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization. Chaos Solitons Fractals 44:137\u2013144","journal-title":"Chaos Solitons Fractals"},{"key":"1539_CR15","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s11432-008-0024-2","volume":"51","author":"X Liao","year":"2008","unstructured":"Liao X, Fu Y, Xie S, Yu P (2008) Globally exponentially attractive sets of the family of Lorenz systems. Sci China Ser F 51:283\u2013292","journal-title":"Sci China Ser F"},{"key":"1539_CR16","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1088\/0951-7715\/16\/5\/303","volume":"16","author":"A Pogromsky","year":"2003","unstructured":"Pogromsky A, Santoboni G, Nijmeijer H (2003) An ultimate bound on the trajectories of the Lorenz system and its applications. Nonlinearity 16:1597\u20131605","journal-title":"Nonlinearity"},{"key":"1539_CR17","first-page":"1","volume":"13","author":"G Leonov","year":"2001","unstructured":"Leonov G (2001) Lyapunov dimension formulas for Henon and Lorenz attractors. St. Petersburg Math J 13:1\u201312","journal-title":"St. Petersburg Math. J."},{"key":"1539_CR18","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.jappmathmech.2012.05.002","volume":"76","author":"G Leonov","year":"2012","unstructured":"Leonov G (2012) Lyapunov functions in the attractors dimension theory. J Appl Math Mech 76:129\u2013141","journal-title":"J Appl Math Mech"},{"key":"1539_CR19","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1007\/s11071-011-0159-3","volume":"67","author":"J Zhang","year":"2012","unstructured":"Zhang J, Tang W (2012) A novel bounded 4D chaotic system. Nonlinear Dyn 67:2455\u20132465","journal-title":"Nonlinear Dyn"},{"issue":"20","key":"1539_CR20","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1016\/j.physleta.2009.03.032","volume":"373","author":"CK Ahn","year":"2009","unstructured":"Ahn CK (2009) An H $$\\infty$$ \u221e approach to anti-synchronization for chaotic systems. Phys Lett A 373(20):1729\u20131733","journal-title":"Phys Lett A"},{"key":"1539_CR21","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/s11071-013-0804-0","volume":"73","author":"S Effati","year":"2013","unstructured":"Effati S, Saberi Nik H, Jajarmi A (2013) Hyperchaos control of the hyperchaotic Chen system by optimal control design. Nonlinear Dyn 73:499\u2013508","journal-title":"Nonlinear Dyn"},{"key":"1539_CR22","doi-asserted-by":"crossref","unstructured":"Effati S, Saberi-Nadjafi J, Saberi Nik H (2013) Optimal and adaptive control for a kind of 3D chaotic and 4D hyper-chaotic systems. Appl Math Model 38:759\u2013774","DOI":"10.1016\/j.apm.2013.06.025"},{"key":"1539_CR23","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.ijengsci.2005.08.003","volume":"44","author":"I Kunin","year":"2006","unstructured":"Kunin I, Chernykh G, Kunin B (2006) Optimal chaos control and discretization algorithms. Int J Eng Sci 44:59\u201366","journal-title":"Int J Eng Sci."},{"key":"1539_CR24","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0960-0779(02)00116-9","volume":"15","author":"S Lenci","year":"2003","unstructured":"Lenci S, Rega G (2003) Optimal numerical control of single-well to cross-well chaos transition in mechanical systems. Chaos Solitons Fractals 15:173\u2013186","journal-title":"Chaos Solitons Fractals"},{"key":"1539_CR25","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/j.chaos.2008.02.003","volume":"41","author":"A El-Gohary","year":"2009","unstructured":"El-Gohary A (2009) Chaos and optimal control of equilibrium states of tumor system with drug. Chaos Solitons Fractals 41:425\u2013435","journal-title":"Chaos Solitons Fractals"},{"key":"1539_CR26","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1016\/j.chaos.2009.04.028","volume":"42","author":"A El-Gohary","year":"2009","unstructured":"El-Gohary A, Alwasel IA (2009) The chaos and optimal control of cancer model with complete unknown parameters. Chaos Solitons Fractals 42:2865\u20132874","journal-title":"Chaos Solitons Fractals"},{"key":"1539_CR27","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1016\/j.chaos.2006.10.060","volume":"37","author":"A El-Gohary","year":"2008","unstructured":"El-Gohary A (2008) Chaos and optimal control of cancer self-remission and tumor system steady states. Chaos Solitons Fractals 37:1305\u20131316","journal-title":"Chaos Solitons Fractals"},{"issue":"4","key":"1539_CR28","first-page":"13","volume":"6","author":"P He","year":"2013","unstructured":"He P, Jing CG, Fan T, Chen CZ (2013) Outer synchronization of complex networks with multiple coupling time-varying delays. Int J Control Autom 6(4):13\u201332","journal-title":"Int J Control Autom"},{"key":"1539_CR29","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.aml.2012.01.027","volume":"26","author":"AH Bhrawy","year":"2013","unstructured":"Bhrawy AH, Alofi AS (2013) The operational matrix of fractional integration for shifted Chebyshev polynomials. Appl Math Lett 26:25\u201331","journal-title":"Appl Math Lett"},{"key":"1539_CR30","doi-asserted-by":"crossref","unstructured":"Saberi Nik H, Effati S, Motsa SS, Shateyi S (2013) A new piecewise-spectral homotopy analysis method for solving chaotic systems of initial value problems. Math Probl Eng","DOI":"10.1155\/2013\/583193"},{"issue":"4","key":"1539_CR31","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.camwa.2011.12.050","volume":"64","author":"EH Doha","year":"2012","unstructured":"Doha EH, Bhrawy AH (2012) An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method. Comput Math Appl 64(4):558\u2013571","journal-title":"Comput Math Appl"},{"key":"1539_CR32","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.amc.2013.07.056","volume":"222","author":"AH Bhrawy","year":"2013","unstructured":"Bhrawy AH (2013) A Jacobi\u2013Gauss\u2013Lobatto collocation method for solving generalized Fitzhugh\u2013Nagumo equation with time-dependent coefficients. Appl Math Comput 222:255\u2013264","journal-title":"Appl Math Comput"},{"key":"1539_CR33","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1016\/j.physleta.2010.01.030","volume":"374","author":"S Dadras","year":"2010","unstructured":"Dadras S, Momeni HR (2010) Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system. Phys Lett A 374:1368\u20131373","journal-title":"Phys Lett A"},{"key":"1539_CR34","volume-title":"Nonlinear systems","author":"HK Khalil","year":"2002","unstructured":"Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice Hall, Upper Saddle River","edition":"3"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-013-1539-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-013-1539-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-013-1539-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T11:25:40Z","timestamp":1565004340000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-013-1539-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,29]]},"references-count":34,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["1539"],"URL":"https:\/\/doi.org\/10.1007\/s00521-013-1539-z","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,29]]}}}