×

Generate \(n\)-scroll attractor in linear system by scalar output feedback. (English) Zbl 1041.37045

Summary: We propose a method for designing chaos generators. For a linear system we can design a switching scalar output feedback controller such that the control system exhibits chaotic behavior in form of an \(n\)-scroll attractor. We present some examples with numerical simulations that illustrate the efficiency of our method.

MSC:

37N35 Dynamical systems in control
93B52 Feedback control
93C05 Linear systems in control theory
94C05 Analytic circuit theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lorenz, E. N., Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141 (1963) · Zbl 1417.37129
[2] Rössler, O. E., Continuous chaos: four prototype equations, Ann. N. Y. Acad. Sci., 316, 376-392 (1979) · Zbl 0437.76055
[3] Chua, L. O.; Komuro, M.; Matsumato, T., The double scroll family, IEEE Trans. Circuits Syst., CAS-33, 1073-1118 (1986) · Zbl 0634.58015
[4] Cannas, B.; Cincotti, S.; Marchesi, M.; Pilo, F., Learning of Chua’s circuit attractors by locally recurrent neural networks, Chaos, Solitons & Fractals, 12, 2109-2115 (2001) · Zbl 0981.68135
[5] Gakkhar, S.; Kamel Naji, R., Chaos in three species ratio dependent food chain, Chaos, Solitons & Fractals, 14, 771-778 (2002) · Zbl 0994.92037
[6] Bai, Er-Wei; Lonngren, K. E.; Sprott, J. C., On the synchronization of a class of electronic circuits that exhibit chaos, Chaos, Solitons & Fractals, 13, 1515-1521 (2002) · Zbl 1005.34041
[7] Stynes, D.; Heffernan, D. M., Universality and scaling in chaotic attractor-to-chaotic attractor transitions, Chaos, Solitons & Fractals, 13, 1195-1204 (2002) · Zbl 1067.37048
[8] Lorenz, H.-W.; Nusse, H. E., Chaotic attractors, chaotic saddles, and fractal basin boundaries: Goodwin’s nonlinear accelerator model reconsidered, Chaos, Solitons & Fractals, 13, 957-965 (2002) · Zbl 1016.37052
[9] Kennedy, M. P.; Kolumban, G., Introduction to the special issue on noncoherent chaotic communications, IEEE Trans. Circ. Syst., 47, 1661 (2000) · Zbl 0976.00020
[10] Brown, R., Generalization of the Chua equations, IEEE Trans. Circ. Syst., I, 40, 11, 878-884 (1993) · Zbl 0847.58053
[11] Suykens, J. A.K.; Vandewalle, J., Generation of \(n\)-double scrolls \((n=1,2,3,4\),…), IEEE Trans. Circ. Syst., I, 40, 11, 861-867 (1993) · Zbl 0844.58063
[12] Yalcin, M. E.; Ozoguz, S.; Suykens, J. A.K.; Vandewalle, J., \(n\)-scroll chaos generators: a simple circuit model, Electron. Lett., 37, 3, 147-148 (2001)
[13] Yang, X.-S.; Li, Q., Chaos generator via Wien-bridge oscillator, Electron. Lett., 38, 623-625 (2002)
[14] Yang, X.-S.; Li, Q., Chaotic attractor in a hybrid system, Int. J. Bifurcation Chaos, 12, 2255-2256 (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.