×
Wang, Xuedi; Tian, Lixin

Bifurcation analysis and linear control of the Newton–Leipnik system. (English) Zbl 1091.93031

Chaos Solitons Fractals 27, No. 1, 31-38 (2006).
Summary: We study a sort of chaotic system – Newton-Leipnik system which possesses two strange attractors. The static and dynamic bifurcations of the system are studied. The chaos controlling is performed by a simpler linear controller, and numerical simulation of the control is supplied. At the same time, Lyapunov exponents of the system show that the result of the chaos controlling is right.

Cited in 10 Documents

MSC:

93D15 Stabilization of systems by feedback
34C23 Bifurcation theory for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

Lyapunov exponents
PDF BibTeX XML Cite
\textit{X. Wang} and \textit{L. Tian}, Chaos Solitons Fractals 27, No. 1, 31--38 (2006; Zbl 1091.93031)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Chen, G.; Moiola, J.; Wang, H., Bifurcation control: theories, methods, and applications, Int J bifur chaos, 10, 3, 511-548, (2000) · Zbl 1090.37552
[2] Ueta, T.; Chen, G., Bifurcation analysis of chen’s equation, Int J bifur chaos, 10, 8, 1917-1931, (2000) · Zbl 1090.37531
[3] Liu, S.; Chen, G., Nonlinear feedback-controlled generalized synchronization of spatial chaos, Chaos, solitons & fractals, 22, 35-46, (2004) · Zbl 1060.93531
[4] Wang, X.; Tian, L., Tracing control of chaos for the coupled dynamos dynamical system, Chaos, solitons & fractals, 21, 4, 193-200, (2004) · Zbl 1045.37017
[5] Yu, Y.; Zhang, S., Controlling uncertain system using back stepping design, Chaos, solitons & fractals, 15, 897-902, (2003) · Zbl 1033.37050
[6] Liu, F.; Ren, Y.; Shan, X.; Qiu, Z., A linear feedback synchronization theorem for a class of chaotic systems, Chaos, solitons & fractals, 13, 4, 723-730, (2002) · Zbl 1032.34045
[7] Lü, J.; Zhou, T.; Zhang, S., Chaos synchronization between linearly chaotic systems, Chaos, solitons & fractals, 14, 4, 529-541, (2002) · Zbl 1067.37043
[8] Richter, H., Controlling chaotic system with multiple strange attractors, Phys lett A, 300, 182-188, (2002) · Zbl 0997.37012
[9] Wolf, A.; Swift, J.; Swinney, H.; Vastano, J., Determining Lyapunov exponents from a time series, Physica D, 16, 285-317, (1985) · Zbl 0585.58037
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.