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Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller. (English) Zbl 1197.37032

Summary: This paper examines chaos control of two four-dimensional chaotic systems, namely: the Lorenz-Stenflo (LS) system that models low-frequency short-wavelength gravity waves and a new four-dimensional chaotic system (Qi systems), containing three cross products. The control analysis is based on recursive backstepping design technique and it is shown to be effective for the 4D systems considered. Numerical simulations are also presented.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and applications, (1998), World Scientific Singapore
[2] Kapitaniak, T., Controlling chaos: theoretical and practical methods in nonlinear dynamics, (1996), Academic Press London · Zbl 0883.58021
[3] Lakshmanan, M.; Murali, K., Chaos in nonlinear oscillators: controlling and synchronization, (1996), World Scientific Singapore · Zbl 0868.58058
[4] Boccaletti, S.; Grebogi, C.; Lai, Y.-C.; Mancini, H.; Maza, D., Phys rep, 329, 103, (2000)
[5] Ott, E.; Grebogi, C.; Yorke, J.A., Phys rev lett, 64, 1196, (1990)
[6] Pyragas, K.; Pyragas, K.; Tawagoshi, A.; Pyragas, K., Phys lett A, Phys lett A, Phys rev lett, 86, 2265, (2001)
[7] Ditto, W.; Rauseo, S.; Spano, M., Phys rev lett, 65, 3211, (1990)
[8] Hunt, E., Phys rev lett, 67, 1953, (1991)
[9] Roy, R., Phys rev lett, 68, 1259, (1992)
[10] Parmananda, P.; Shavard, P.; Rolins, R.; Dewald, H., Phys rev E, 47, 3003, (1993)
[11] Wiener, R.; Dolby, D.C.; Gibbs, G.; Squirer, B.; Olson, T.; Smily, A., Phys rev lett, 83, 2340, (1999)
[12] Lüthje, O.; Woltt, S.; Pfisker, G., Phys rev lett, 86, 1745, (2001)
[13] Pyragas, K.; Tamasiavicius, A.; Gauthier, D.; Sukow, D.W.; Concannon, H.M.; Socolar, J.E.S., Phys lett A, Phys rev E, 50, 2343, (1994)
[14] Hikihara, T.; Kawagoshi, T.; Christini, D.J.; In, V.; Spano, M.; Ditto, W.; Collins, J.J., Phys lett A, Phys rev E, 56, R3743, (1997)
[15] Bielawski, B.; Derozier, D.; Glorieux, P.; Lu, W.; Yu, D.; Harrison, R.G., Phys rev E, Int J bifurcat chaos, 8, 1769, (1998)
[16] Parmanada, P.; Madrigal, R.; Rivers, M.; Nykios, L.; Kiss, Z.; Garpar, V., Phys rev E, 59, 5266, (1999)
[17] Special Issue on “Chaos in nonlinear electronic circuits, IEEE Trans. on CAS, vol. 40, Part I & II, No. 10 Part I No. 11; 1993.
[18] Gills, Z.; Iwata, C.; Roy, R.; Swartz, I.B.; Triandaf, I., Phys rev lett, 78, 3169, (1992)
[19] Just, W.; Bernard, T.; Ostheimer, M.; Reibold, E.; Benner, H., Phys rev lett, 78, 203, (1997)
[20] Chen, G.; Yu, X., IEEE trans circ syst I, 46, 767, (1999)
[21] Guan, X.; Chen, C.; Fan, Z.; Peng, H., Int J bifurcat chaos, 13, 193, (2003)
[22] Ercan, S.; Omar, M.; Umut, E.W., Phys lett A, 279, 47, (2001)
[23] Ghezzi, L.L.; Piccardi, C., Automatica, 33, 181, (1997)
[24] Konishi, K.; Hirai, M.; Kokame, H., Phys lett A, 245, 571, (1998)
[25] Jang, M., Int J bifurcat chaos, 12, 1437, (2002)
[26] Yu, X., Chaos, solitons & fractals, 8, 1577, (1997)
[27] Harb, A.M., Chaos, solitons & fractals, 19, 1217, (2004) · Zbl 1072.78512
[28] Harb, A.M.; Harb, B.A., Chaos, solitons & fractals, 20, 719, (2004) · Zbl 1245.93058
[29] Yongguang, Y.; Suochun, Z., Chaos, solitons & fractals, 15, 897, (2003)
[30] Ge, S.S.; Wang, C.; Lee, T.H., Int J bifurcat chaos, 10, 1149, (2000)
[31] Zhang, H.; Ma, X.-K.; Li, M.; Zou, J.-L., Chaos, solitons & fractals, 26, 353, (2005)
[32] Kotkotovic, P.V., IEEE control syst mag, 6, 7, (1992)
[33] Kristic, M.; Kanellakopoulus, I.; Kokotovic, P., Nonlinear and adaptive control, (1995), John Wiley and Sons Inc.
[34] Stenflo, L., Phys scripta, 53, 83, (1996)
[35] Zhaou, C.; Lai, C.H.; Yu, M.Y., J math phys, 38, 5225, (1997)
[36] Liu, Z., Phys scripta, 61, 526, (2000)
[37] Banerjee, S.; Saha, P.; Chowdhury, A.R., Phys scripta, 63, 177, (2001)
[38] Banerjee, S.; Saha, P.; Chowdhury, A.R., Int J nonlinear mech, 39, 25, (2004)
[39] Qi, G.; Chen, Z.; Du, S.; Yuan, Z., Chaos solitons & fractals, 23, 1671, (2005)
[40] Vincent, U.E., Synchronization of identical and non-identical 4-D chaotic systems using active control, Chaos, solitons & fractals, 37, 4, 1065, (2008) · Zbl 1153.37359
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