Xu, Yuhua; Zhou, Wuneng; Fang, Jian-An; Ma, Junhai; Wang, Yuling Generating a new chaotic attractor by feedback controlling method. (English) Zbl 1230.37111 Math. Methods Appl. Sci. 34, No. 17, 2159-2166 (2011). 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. Cited in 2 Documents MSC: 37N35 Dynamical systems in control 93B05 Controllability 93B52 Feedback control Keywords:chaos; Lorenz system; Chen’s system; Lü system; Liu system PDF BibTeX XML Cite \textit{Y. Xu} et al., Math. Methods Appl. Sci. 34, No. 17, 2159--2166 (2011; Zbl 1230.37111) Full Text: DOI References: [1] Lorenz, Deterministic non-periodic flows, Journal of the Atmospheric Sciences 20 pp 130– (1963) · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 [2] Rössler, An equation for continuous chaos, Physics Letter A 57 (4) pp 397– (1976) · Zbl 1371.37062 · doi:10.1016/0375-9601(76)90101-8 [3] Chen, Yet another chaotic attractor, International Journal of Bifurcation and Chaos 9 (6) pp 1465– (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024 [4] Lü, A new chaotic attractor coined, International Journal of Bifurcation and Chaos 12 (2) pp 659– (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620 [5] Liu, A new chaotic attractor, Chaos, Solitons and Fractals 22 pp 1031– (2004) · Zbl 1060.37027 · doi:10.1016/j.chaos.2004.02.060 [6] Celikovsky, On the generalized Lorenz canonical form, Chaos Solitons and Fractals 26 pp 1271– (2005) · Zbl 1100.37016 · doi:10.1016/j.chaos.2005.02.040 [7] Chen, Generating hyperchaotic Lü attractor via state feedback control, Physica A 364 pp 103– (2006) · doi:10.1016/j.physa.2005.09.039 [8] Zhou, On dynamics analysis of a new chaotic attractor, Physics Letter A 372 pp 5773– (2008) · Zbl 1223.37045 · doi:10.1016/j.physleta.2008.07.032 [9] Wolf, Determining Lyapunov exponents from a time series, Physica D 16 pp 285– (1985) · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9 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.