×

zbMATH — the first resource for mathematics

A topological horseshoe in the hyperchaotic Rössler attractor. (English) Zbl 1220.37023
Summary: This Letter reports a horseshoe with two-directional expansion in the 4D hyperchaotic Rössler system. In order to show that it is indeed a horseshoe with two-dimensional expansion, some simple results on topological horseshoe which are applicable to 3D hyperchaotic maps are presented. In this way, a computer-assisted verification of hyperchaoticity is presented.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Wiggins, S., Introduction to applied nonlinear dynamical systems and chaos, (1990), Springer-Verlag New York · Zbl 0701.58001
[2] Szymczak, A., Topology, 35, 2, 287, (1996)
[3] Kennedy, J.; Yorke, J.A., Trans. am. math. soc., 353, 6, 2513, (2001)
[4] Zgliczyński, P.; Gidea, M., J. differential equations, 202, 1, 33, (2004)
[5] Yang, X.-S.; Tang, Y., Chaos solitons fractals, 19, 4, 841, (2004)
[6] Yang, X.-S., Chaos solitons fractals, 20, 1149, (2004)
[7] Yang, X.-S., Chaos solitons fractals, 33, 1, 225, (2007)
[8] Yang, X.-S.; Li, H.; Huang, Y., J. phys. A: math. gen., 38, 4175, (2005)
[9] Rössler, O.E., Phys. lett. A, 60, 5, 392, (1977)
[10] Zgliczyński, P., Nonlinearity, 10, 243, (1997)
[11] Yang, X.-S.; Yu, Y.; Zhang, S., Chaos solitons fractals, 18, 223, (2003)
[12] Yang, X.-S.; Li, Q., Int. J. bifur. chaos, 15, 5, 1823, (2005)
[13] Yang, X.-S.; Yang, F., Chaos solitons fractals, 20, 2, 587, (2004)
[14] Yang, X.-S.; Tang, Y.; Li, Q., Chaos solitons fractals, 21, 5, 1087, (2004)
[15] Huang, Y.; Yang, X.-S., J. math. chem., 38, 1, 1823, (2005)
[16] Yang, X.-S.; Li, Q., Int. J. bifur. chaos, 14, 5, 1847, (2004)
[17] Yang, X.-S.; Tang, Y., Chaos solitons fractals, 23, 87, (2005)
[18] Yang, X.-S.; Li, Q., Chaos solitons fractals, 27, 25, (2006)
[19] Yang, X.-S.; Li, Q., Int. J. bifur. chaos, 16, 1, 131, (2006)
[20] Matsumoto, T.; Chua, L.O.; Kobayashi, K., IEEE trans. circuits syst., 33, 11, 1143, (1986)
[21] Udaltsov, V.S.; Goedgbuer, J.-P.; Larger, L.; Rhodes, W.T., Phys. rev. lett., 86, 9, 1892, (2001)
[22] Li, Q.; Yang, X.-S.; Yang, F., Neurocomputing, 67, 275, (2005)
[23] Yang, L.; Liu, Z.; Mao, J.-m., Phys. rev. lett., 84, 1-3, 67, (2000)
[24] Grassi, G.; Mascolo, S., Electron. lett., 34, 5, 424, (1998)
[25] Miller, D.A.; Grassi, G., IEEE trans. circuits syst. fund. theor. appl., 48, 3, 366, (2001)
[26] Rössler, O.E., Phys. lett. A, 71, 2-3, 155, (1979)
[27] Heath, M.T., Scientific computing, an introductory survey, (2002), McGraw-Hill New York · Zbl 0903.68072
[28] Guckenheimer, J.; Oliva, R.A., SIAM J. appl. dyn. syst., 1, 1, 105, (2002)
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.