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Wei, Zhouchao

Dynamical behaviors of a chaotic system with no equilibria. (English) Zbl 1255.37013

Phys. Lett., A 376, No. 2, 102-108 (2011).
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.

Cited in 111 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M10 Time series analysis of dynamical systems
93B05 Controllability
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)

Keywords:

Sprott D system; chaotic attractors; no equilibria; bifurcation diagram; period-doubling cascade
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\textit{Z. Wei}, Phys. Lett., A 376, No. 2, 102--108 (2011; Zbl 1255.37013)
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References:

[1] Lorenz, E.N., J. atmos. sci., 20, 130, (1963)
[2] Rössler, O.E., Phys. lett. A, 57, 397, (1976)
[3] Chen, G.R.; Ueta, T., Int. J. bifur. chaos, 9, 1465, (1999)
[4] Lü, J.H.; Chen, G.R., Int. J. bifur. chaos, 12, 659, (2002)
[5] Sprott, J.C., Phys. rev. E, 50, 647, (1994)
[6] Silva, C.P., IEEE trans. circ. syst. I, 40, 657, (1993)
[7] Yang, Q.G.; Wei, Z.C.; Chen, G.R., Int. J. bifur. chaos, 20, 1061, (2010)
[8] Yang, Q.G.; Chen, G.R., Int. J. bifur. chaos, 18, 1393, (2008)
[9] Wang, X.; Chen, G.R., Commun. nonlinear sci. numer. simulat., 17, 1264, (2012)
[10] Falkner, V.M.; Skan, S.W., Philosophical magazine, 7, 865, (1931)
[11] Kuznetsov, Y.A., Elements of applied bifurcation theory, (1998), Springer New York · Zbl 0914.58025
[12] Hou, Z.T.; Kang, N.; Kong, X.X.; Chen, G.R.; Yan, G.J., Int. J. bifur. chaos, 20, 557, (2010)
[13] Poincaré, H., Acta Mathematica, 13, 1, (1890)
[14] Bendixson, I., Acta Mathematica, 24, 1, (1901)
[15] Barnett, S., Polynomials and linear control systems, (1983), Marcel Dekker, Inc. New York · Zbl 0528.93003
[16] Feigenbaum, M.J., Physica D, 7, 16, (1983)
[17] Haniasa, M.P.; Avgerinos, Z.; Tombras, G.S., Chaos solitons fractals, 40, 1050, (2009)
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.