The generation and circuit implementation of a new hyper-chaos based upon Lorenz system. (English) Zbl 1170.37308

Summary: This Letter presents a new hyper-chaotic system, which was obtained by adding a nonlinear quadratic controller to the second equation of the three-dimensional autonomous modified Lorenz chaotic system. The resulting hyper-chaotic system undergoes a change from hyper-chaos to limit cycle with some of its parameters changed. The phenomena were demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. The experiment results of the hyper-chaotic circuit were well agreed with the simulation results.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


[1] Genys, A.; Tamasevicius, A.; Baziliauskas, A.; Krivickas, R.; Lindberg, E., Chaos Solitons Fractals, 17, 349 (2003) · Zbl 1036.94505
[2] Cafagna, D.; Grassi, G., Int. J. Bifur. Chaos, 13, 2889 (2003) · Zbl 1057.37026
[3] Udaltsov, V. S.; Goedgebuer, J. P.; Larger, L., Opt. Spectrosc., 95, 114 (2003)
[4] Grassi, G.; Mascolo, S., J. Circuits Syst. Comput., 11, 1 (2002)
[5] Brucoli, M.; Carnimeo, L.; Grassi, L., Int. J. Bifur. Chaos, 6, 1673 (1996) · Zbl 0873.94002
[6] Rössler, O. E., Phys. Lett. A, 71, 155 (1979) · Zbl 0996.37502
[7] Goedgebuer, J. P.; Larger, L.; Port, H., Phys. Rev. Lett., 80, 2249 (1998)
[8] Li, Y.; Tang, W. K.S.; Chen, G., Int. J. Circuits Theor. Appl., 33, 235 (2005) · Zbl 1079.34032
[9] Kapitaniak, T.; Chua, L. O., Int. J. Bifur. Chaos, 4, 477 (1994) · Zbl 0813.58037
[10] Li, Y.; Tang, W. K.S.; Chen, G., IEEE Trans. Circuits Systems II, 52, 204 (2005)
[11] Li, Y.; Tang, W. K.S.; Chen, G., Int. J. Bifur. Chaos, 15, 3367 (2004)
[12] Celikovsky, S.; Chen, G., Chaos Solitons Fractals, 26, 1271 (2005) · Zbl 1100.37016
[13] Murali, K.; Lindberg, E.; Leung, H., AIP Conf. Proc, 622, 15 (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.