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Yang and yin parameters in the Lorenz system. (English) Zbl 1210.34065

From the summary: The chaos in the historical Lorenz system with “Yin parameters” is introduced and various kinds of phenomena in the historical Lorenz system are investigated by Lyapunov exponents, phase portraits, and bifurcation diagrams.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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[1] Lacitignola, D., Petrosillo, I., Zurlini, G.: Time-dependent regimes of a tourism-based social–ecological system: period-doubling route to chaos. Ecol. Complex. 7, 44–54 (2010) · doi:10.1016/j.ecocom.2009.03.009
[2] Elnashaie, S.S.E.H., Grace, J.R.: Complexity, bifurcation and chaos in natural and man-made lumped and distributed systems. Chem. Eng. Sci. 62, 3295–3325 (2007) · doi:10.1016/j.ces.2007.02.047
[3] Jovic, B., Unsworth, C.P., Sandhu, G.S., Berber, S.M.: A robust sequence synchronization unit for multi-user DS-CDMA chaos-based communication systems. Signal Process. 87, 1692–1708 (2007) · Zbl 1186.94166 · doi:10.1016/j.sigpro.2007.01.014
[4] Ge, Z.M., Chen, C.C.: Phase synchronization of coupled chaotic multiple time scales systems. Chaos Solitons Fractals 20, 639–647 (2004) · Zbl 1069.34056 · doi:10.1016/j.chaos.2003.08.001
[5] Ge, Z.M., Cheng, J.W.: Chaos synchronization and parameter identification of three time scales brushless DC motor system. Chaos Solitons Fractals 24, 597–616 (2005) · Zbl 1061.93524 · doi:10.1016/j.chaos.2004.09.031
[6] Wang, Y., Wong, K.W., Liao, X., Chen, G.: A new chaos-based fast image encryption algorithm. Appl. Soft Comput. (in press)
[7] Fallahi, K., Leung, H.: A chaos secure communication scheme based on multiplication modulation. Commun. Nonlinear Sci. Numer. Simul. 15, 368–383 (2010) · Zbl 1221.94045 · doi:10.1016/j.cnsns.2009.03.022
[8] Yu, W.: A new chaotic system with fractional order and its projective synchronization. Nonlinear Dyn. 48, 165–174 (2007) · Zbl 1176.92008 · doi:10.1007/s11071-006-9080-6
[9] Chen, H.K., Sheu, L.J.: The transient ladder synchronization of chaotic systems. Phys. Lett. A 355, 207–211 (2006) · doi:10.1016/j.physleta.2005.10.111
[10] Lorenz, E.N.: Deterministic non-periodic flows. J. Atoms. 20, 130–141 (1963) · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[11] Cox, S.M.: The transition to chaos in an asymmetric perturbation of the Lorenz system. Phys. Lett. A 144, 325–328 (1990) · doi:10.1016/0375-9601(90)90134-A
[12] Chen, C.-C., Tsai, C.-H., Fu, C.-C.: Rich dynamics in self-interacting Lorenz systems. Phys. Lett. A 194, 265–271 (1994) · Zbl 0959.37509 · doi:10.1016/0375-9601(94)91248-3
[13] Liu, Y., Barbosa, L.C.: Periodic locking in coupled Lorenz systems. Phys. Lett. A 197, 13–18 (1995) · Zbl 1020.37509 · doi:10.1016/0375-9601(94)00887-U
[14] Wang, L.: 3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system. Nonlinear Dyn. 56, 453–462 (2009) · Zbl 1204.70021 · doi:10.1007/s11071-008-9417-4
[15] Cang, S., Qi, G., Chen, Z.: A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dyn. 59, 515–527 (2010) · Zbl 1183.70049 · doi:10.1007/s11071-009-9558-0
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