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)
Dynamical behaviors of a chaotic system with no equilibria. (English) Zbl 1255.37013
Summary: Based on the Sprott D system, a simple three-dimensional autonomous system with no equilibria is reported. The remarkable particularity of the system is that there exists a constant controller, which can adjust the type of chaotic attractors. It is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent and fractional dimension. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcation diagram, Poincaré mapping and period-doubling route to chaos are analyzed with careful numerical simulations.
MSC:
37D45Strange attractors, chaotic dynamics
37M10Time series analysis (dynamical systems)
93B05Controllability
37M25Computational methods for ergodic theory
References:
[1]Lorenz, E. N.: J. atmos. Sci., J. atmos. Sci. 20, 130 (1963)
[2]Rössler, O. E.: Phys. lett. A, Phys. lett. A 57, 397 (1976)
[3]Chen, G. R.; Ueta, T.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 9, 1465 (1999)
[4]Lü, J. H.; Chen, G. R.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 12, 659 (2002)
[5]Sprott, J. C.: Phys. rev. E, Phys. rev. E 50, 647 (1994)
[6]Silva, C. P.: IEEE trans. Circ. syst. I, IEEE trans. Circ. syst. I 40, 657 (1993)
[7]Yang, Q. G.; Wei, Z. C.; Chen, G. R.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 20, 1061 (2010)
[8]Yang, Q. G.; Chen, G. R.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 18, 1393 (2008)
[9]Wang, X.; Chen, G. R.: Commun. nonlinear sci. Numer. simulat., Commun. nonlinear sci. Numer. simulat. 17, 1264 (2012)
[10]Falkner, V. M.; Skan, S. W.: Philosophical magazine, Philosophical magazine 7, 865 (1931)
[11]Kuznetsov, Y. A.: Elements of applied bifurcation theory, (1998)
[12]Hou, Z. T.; Kang, N.; Kong, X. X.; Chen, G. R.; Yan, G. J.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 20, 557 (2010)
[13]Poincaré, H.: Acta Mathematica, Acta Mathematica 13, 1 (1890)
[14]Bendixson, I.: Acta Mathematica, Acta Mathematica 24, 1 (1901)
[15]Barnett, S.: Polynomials and linear control systems, (1983)
[16]Feigenbaum, M. J.: Physica D, Physica D 7, 16 (1983)
[17]Haniasa, M. P.; Avgerinos, Z.; Tombras, G. S.: Chaos solitons fractals, Chaos solitons fractals 40, 1050 (2009)