×

A new chaotic attractor. (English) Zbl 1060.37027

Summary: A new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincaré mapping, fractal dimension, continuous spectrum and chaotic behaviors of this new butterfly attractor are studied. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation is investigated by detailed numerical as well as theoretical analysis.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Sparrow, C., The Lorenz equations: bifurcations, chaos, and strange attractors (1982), Springer: Springer New York · Zbl 0504.58001
[2] Lü, J.; Chen, G.; Zhang, S., Dynamical analysis of a new chaotic attractor, Int. J. Bifurcat. Chaos, 12, 5, 1001-1015 (2002) · Zbl 1044.37021
[3] Wolf, A.; Swift, J. B.; Swinney, HL; Vastano, J. A., Determining Lyapunov exponents from a time series, Physica D, 16, 285-317 (1985) · Zbl 0585.58037
[4] Ueta, T.; Chen, G., Bifurcation analysis of Chen’s attractor, Int. J. Bifurcat. Chaos, 10, 1917-1931 (2000) · Zbl 1090.37531
[5] Lü, J.; Chen, G.; Zhang, S., The compound structure of a new chaotic attractor, Chaos, Solitons & Fractals, 14, 669-672 (2002) · Zbl 1067.37042
[6] Zhong, G. Q.; Tang, W. K.S., Circuitry implementation and synchronization of Chen’s attractor, Int. J. Bifurcat. Chaos, 12, 6, 1423-1427 (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.