zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the generalized Lorenz canonical form. (English) Zbl 1100.37016
Here, the generalized Lorenz canonical form is introduced and used to classify various recently published chaotic systems. This classification with respect to global nonsingular coordinate transformation and time scaling is summarized as well.

37D45Strange attractors, chaotic dynamics
37A40Nonsingular (and infinite-measure preserving) transformations
Full Text: DOI
[1] Čelikovský, S.; Chen, G.: On a generalized Lorenz canonical form of chaotic systems. Int J bifur chaos 12, 1789-1812 (2002) · Zbl 1043.37023
[2] Čelikovský S, Chen G. Hyperbolic-type generalized Lorenz system and its canonical form. In: Proceedings of the 15th triennial world congress of IFAC, Barcelona, Spain, July 2002, CD ROM.
[3] Čelikovský, S.; Vaněček, A.: Bilinear systems and chaos. Kybernetika 30, 403-424 (1994) · Zbl 0823.93026
[4] Chen, G.; Dong, X.: From chaos to order: methodologies, perspectives, and applications. (1998) · Zbl 0908.93005
[5] Chen, G.; Ueta, T.: Yet another chaotic attractor. Int J bifur chaos 9, 1465-1466 (1999) · Zbl 0962.37013
[6] Li, T. C.; Chen, G.; Tang, Y.: On stability and bifurcation of Chen’s system. Chaos, solitons & fractals 19, 1269-1282 (2004) · Zbl 1069.34060
[7] Lian, K.; Liu, P.: Synchronization with message embedded for generalized Lorenz chaotic circuits and its error analysis. IEEE trans circ syst-I 47, 1418-1424 (2000) · Zbl 1011.94033
[8] Liu, C.; Liu, T.; Liu, L.; Liu, K.: A new chaotic attractor. Chaos, solitons & fractals 22, 1031-1038 (2004) · Zbl 1060.37027
[9] Lorenz, E. N.: Deterministic nonperiodic flow. J atmos sci 20, 130-141 (1963)
[10] Lü, J.; Chen, G.: A new chaotic attractor coined. Int J bifur chaos 12, 659-661 (2002) · Zbl 1063.34510
[11] Lü, J.; Chen, G.; Cheng, D.; Čelikovský, S.: Bridge the gap between the Lorenz system and the Chen system. Int J bifur chaos 12, 2917-2926 (2002) · Zbl 1043.37026
[12] Shilnikov, A. L.; Shilnikov, L. P.; Turaev, D. V.: Normal forms and Lorenz attractors. Int J bifur chaos 3, 1123-1139 (1993) · Zbl 0885.58080
[13] Shimizu, T.; Morioka, N.: On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model. Phys lett A 76, No. 3-4, 201-204 (1976)
[14] Sparrow, C.: The Lorenz equations: bifurcation, chaos, and strange attractor. (1982) · Zbl 0504.58001
[15] Ueta, T.; Chen, G.: Bifurcation analysis of Chen’s equation. Int J bifur chaos 10, 1917-1931 (2000) · Zbl 1090.37531
[16] Vaněček, A.; Čelikovský, S.: Control systems: from linear analysis to synthesis of chaos. (1996) · Zbl 0874.93006
[17] Zhou, T. S.; Chen, G.; Čelikovský, S.: Si’lnikov chaos in the generalized Lorenz canonical form of dynamics systems. Nonlinear dynamics 39, 319-334 (2005) · Zbl 1142.70012
[18] Zhou, T. S.; Chen, G.; Tang, Y.: Chen’s attractor exists. Int J bifur chaos 14, 3167-3178 (2004) · Zbl 1129.37326
[19] Zhou, T. S.; Chen, G.; Tang, Y.: Complex dynamical behaviors of the chaotic Chen’s system. Int J bifur chaos 13, 2561-2574 (2003) · Zbl 1046.37018