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Zbl 1230.37111
Xu, Yuhua; Zhou, Wuneng; Fang, Jian-An; Ma, Junhai; Wang, Yuling
Generating a new chaotic attractor by feedback controlling method. (English)
[J] Math. Methods Appl. Sci. 34, No. 17, 2159-2166 (2011). ISSN 0170-4214; ISSN 1099-1476/e

Summary: A new chaotic system is found in this paper using a feedback controlling method. According to the definition of the generalized Lorenz system, the new chaotic system does not belong to generalized Lorenz systems. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map. The particular interest is that this novel system can generate two one-scroll and one two-scroll chaotic attractors with the variation of a single parameter. The obtained results show clearly that the system is a new chaotic system and deserves a further detailed investigation.

MSC 2000:: *37N35 Dynamical systems in control
93B05 Controllability
93B52 Feedback control

Keywords: chaos; Lorenz system; Chen's system; Lü system; Liu system

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