Symmetry induced oscillations in four-dimensional models deriving from the van der Pol equation

Chaos, Solitons and Fractals

Volumn 21, Issue 1, 2004, Pages 55-61

  López Ruiz, Ricardo ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DISCRETE TIME CONTROL SYSTEMS; ECOLOGY; HARMONIC ANALYSIS; MATHEMATICAL MODELS; NONLINEAR OPTICS; OSCILLATIONS; REYNOLDS NUMBER; SET THEORY; VORTEX FLOW;

OSCILLATORY DYNAMICS; VAN DER POL EQUATIONS;

CHAOS THEORY;

EID: 0942299387     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2003.09.033     Document Type: Article

References (14)

1. Andronov A.A., Vitt A.A., Khaikin S.E. Theory of oscillators. 1989;Dover, New York.
2. Kuramoto Y. Chemical oscillations, waves and turbulence. 1984;Springer-Verlag, Berlin.
3. Winfree A.T. The timing of biological clocks. 1986;Scientific American Library, W.H. Freeman Co.
4. May R.M. Simple mathematical models with very complicated dynamics. Nature. 261:1976;459-467.
5. López-Ruiz R., Pomeau Y. Transition between two oscillation modes. Phys. Rev. E. 55:1997;R3820-R3823.
6. Frisch T., Pomeau Y., Rica S. Transition to dissipation in a model of superflow. Phys. Rev. Lett. 69:1992;1644-1647.
7. Bénard H. Formation de centres de giration a l'arrière d'un obstacle en mouvement. C.R. Acad. Sci. Paris. 147:1908;839.
8. von Kármán Th. Über den Mechanismus des Flüssigkeits und Luftwiderstandes. Gött. Nachr. Math.-Phys. Klasse. 509:1911.
9. Zhang J., Childress S., Libchaber A., Shelley M. Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature. 408:2000;835-839.
10. Hinch E.J. Perturbation methods. 1991;Cambridge University Press, Cambridge.
11. Svelto O. Principles of lasers. 1989;Plenum Press, New York.
12. Franken P.A., Hill A.E., Peters C.W., Weinreich G. Generation of optical harmonics. Phys. Rev. Lett. 7:1961;118-119.
13. Solari H.G., Natiello M.A., Mindlin G.B. Nonlinear dynamics: a two way trip from physics to maths. 1996;IOP Publishing Ltd, Philadelphia.
14. Gilmore R., Lefranc M. Topology of chaos. 2002;John Wiley & Sons, New York.