zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
A three-scroll chaotic attractor. (English) Zbl 1217.37030
Summary: This Letter introduces a new chaotic member to the three-dimensional smooth autonomous quadratic system family, which derived from the classical Lorenz system but exhibits a three-scroll chaotic attractor. Interestingly, the two other scrolls are symmetry related with respect to the $z$-axis as for the Lorenz attractor, but the third scroll of this three-scroll chaotic attractor is around the $z$-axis. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincaré map and chaotic dynamical behaviors of the new chaotic system are investigated, either numerically or analytically. The obtained results clearly show this is a new chaotic system and deserves further detailed investigation.

MSC:
37D45Strange attractors, chaotic dynamics
WorldCat.org
Full Text: DOI
References:
[1] Lorenz, E. N.: J. atmos. Sci.. 20, 130 (1963)
[2] Stewart, I.: Nature. 406, 948 (2000)
[3] Ott, E.: Chaos in dynamical systems. (2002) · Zbl 1006.37001
[4] Chen, G.; Lü, J. H.: Dynamical analysis, control and synchronization of the generalized Lorenz systems family. (2003)
[5] Chen, G.; Wang, X. F.: Chaotification of dynamical systems: theory, methods and applications. (2006)
[6] Gilmore, R.; Lefranc, M.: The topology of chaos. (2002) · Zbl 1019.37016
[7] Shaw, R.: Z. naturforsch. A. 36, 80 (1981)
[8] Rössler, O. E.: Phys. lett. A. 57, 397 (1976)
[9] Rössler, O. E.: Am. (N.Y.) acad. Sci.. 316, 376 (1979)
[10] Sprott, J. C.: Phys. rev. E. 50, R647 (1994)
[11] Sprott, J. C.: Phys. lett. A. 228, 271 (1997)
[12] Sprott, J. C.; Linz, S. J.: Int. J. Chaos theory appl.. 5, 3 (2000)
[13] Letellier, C.; Tsankov, T.; Byrne, G.; Gilmore, R.: Phys. rev. E. 72, 026212 (2005)
[14] Čelikovský, S.; Vaněcek, A.: Kybernetika. 30, No. 4, 403 (1994)
[15] Vaněcek, A.; Čelikovský, S.: Control systems: from linear analysis to synthesis of chaos. (1996) · Zbl 0874.93006
[16] Chen, G.; Ueta, T.: Int. J. Bifur. chaos. 9, 1465 (1999)
[17] Lü, J. H.; Chen, G.: Int. J. Bifur. chaos. 12, 659 (2002)
[18] Celikovsy, S.; Chen, G.: Int. J. Bifur. chaos. 12, 1789 (2002)
[19] Celikovsy, S.; Chen, G.: Chaos solitons fractals. 26, 1271 (2005)
[20] Rucklidge, A. M.: J. fluid mech.. 237, 209 (1992)
[21] Genesio, R.; Tesi, A.: Automatica. 28, No. 3, 531 (1992)
[22] Liu, C.; Liu, T.; Liu, L.; Liu, K.: Chaos solitons fractals. 22, 1031 (2004)
[23] Shilnikov, A. L.: Physica D. 62, 338 (1993)
[24] Matsumoto, T.; Chua, L. O.; Tanaks, S.: Phys. rev. A. 30, 1155 (1984)
[25] Baghious, E.; Jarry, P.: Int. J. Bifur. chaos. 3, No. 1, 201 (1993)
[26] Elwakil, A.; Ozoguz, S.; Kennedy, M.: IEEE trans. Circuits syst. I. 49, 527 (2002)
[27] Ozoguz, S.; Elwakil, A.; Kennedy, M.: Int. J. Bifur. chaos. 12, 1627 (2002)
[28] Elwakil, A.; Ozoguz, S.; Kennedy, M.: Int. J. Bifur. chaos. 13, No. 10, 3093 (2003)
[29] Liu, W. B.; Chen, G.: Int. J. Bifur. chaos. 12, 261 (2003)
[30] Lü, J. H.; Chen, G.; Cheng, D.: Int. J. Bifur. chaos. 14, 1507 (2004)
[31] Birman, J. S.; Williams, R. F.: Topology. 22, 47 (1983)
[32] Gilmore, R.: Rev. mod. Phys.. 70, No. 4, 1455 (1998)
[33] Tsankov, T.; Byrne, G.; Gilmore, R.: Phys. rev. Lett.. 13, 134104 (2003)
[34] Letellier, C.; Roulin, E.; Rössler, O. E.: Chaos solitons fractals. 28, 337 (2006) · Zbl 1084.34048
[35] Miranda, R.; Stone, E.: Phys. lett. A. 178, 105 (1993)
[36] Yu, S.; Lü, J. H.; Wallace, K.; Tangb, S.; Chen, G.: Chaos. 16, No. 3, 033126 (2006)
[37] Wang, X. F.; Chen, G.; Yu, X.: Chaos. 10, 1 (2000) · Zbl 0967.93045
[38] Takagi, T.; Sugeno, M.: IEEE trans. Syst. cybernet.. 15, 116 (1985)
[39] Kivshar, Y. S.; Rodelsperger, F.; Benner, H.: Phys. rev. E. 39, 319 (1994)
[40] Li, D. Q.: Chin. phys.. 15, No. 11, 2541 (2006)
[41] Li, D. Q.: Phys. lett. A. 356, No. 1, 51 (2006)
[42] D.Q Li, Z. Yin, Exploring the compound structure of chaotic Chen’s attractor: A hybrid TS fuzzy approach, Chaos Solitons Fractals (2007), in press
[43] Wolf, A.; Swift, J. B.; Swinney, H. L.; Vastano, J. A.: Physica D. 16, 285 (1985)