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Patterns of Aperiodic Pulsation

Published online by Cambridge University Press:  12 April 2016

E. A. Spiegel
E. A. Spiegel*
Affiliation:
Astronomy Department, Columbia University, New York, NY 10027, USA

Abstract

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Techniques for deriving amplitude equations for stellar pulsation are outlined. For the simplest such equations with multiple instabilities, the derivation of a map for the patterns of pulsation phases is described. This map gives the time between two successive maxima of pulsation in terms of the time between the previous pair, under suitable conditions. The phase differences can be regular, chaotic or hyperchaotic.

Type
I. Fundamental Theories
Information
International Astronomical Union Colloquium , Volume 134: Nonlinear Phenomena in Stellar Variability , 1993 , pp. 33 - 49
Copyright
Copyright © Kluwer 1993

References

Arneodo, A., Coullet, P.H. and Spiegel, E.A.: 1982, “Chaos in a Finite Macroscopic System,” Phys. Lett. A92, 368.Google Scholar
Arneodo, A., Coullet, P.H., Spiegel, E.A. and Tresser, C.: 1985a, “Asymptotic Chaos,” Physica D14, 327.Google Scholar
Arneodo, A., Coullet, P.H. and Spiegel, E.A.: 1985b, “The Dynamics of Triple Convection,” Geophys. and Astrophys. Fluid Dynamics 31, 1.Google Scholar
Baker, N.H.: 1966, “Simplified models for Cepheid instability,” in Stellar Evolution, eds. Stein, R.F. and Cameron, A.G.W. (Plenum Press). 333–346.Google Scholar
Baker, N.H., Moore, D.W. and Spiegel, E.A.: 1966, “Nonlinear Oscillations in the One-Zone Model for Stellar Pulsation,” Astronomical Journal 71, 845.Google Scholar
Baker, N.H., Moore, D.W. and Spiegel, E.A.: 1971, “Aperiodic Behavior of a Non-Linear Oscillator,” Quart. Jour. Mech. Appl Math. 24, 391.Google Scholar
Carr, J.: 1981, Applications of Centre Manifold Theory, (Spring-Verlarg).Google Scholar
Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, (Oxford Univ. Press).Google Scholar
Coullet, P.H. and Elphick, C.: 1987, “Topological defect dynamics and Melniknov’s theory,” Phys. Lett. A121, 233.Google Scholar
Coullet, P.H. and Spiegel, E.A.: 1981, “A Tale of Two Methods,” in Summer Study Program in Geophysical Fluid Dynamics, The Woods Holes Oceanographic Institution, ed. Mellor, F.k., p. 276.Google Scholar
Coullet, P.H. and Spiegel, E.A.: 1983, “Amplitude Equations for Systems With Competing Instabilities,” SIAM.J. Appl. Math. 43, 774.Google Scholar
Elphick, C., Meron, E. and Spiegel, E.A.: 1990a, “Patterns of Propagating Pulses,” SIAM J. Appl. Math. 50, 490.Google Scholar
Elphick, C., Meron, E., Rinzel, J. and Spiegel, E.A.: 1990b, “Impulse patterning and relaxational propagation in excitable media,” J. Theor. Biol. 146, 249.Google Scholar
Elphick, C., Regev, O., Ierley, G.R. and Spiegel, E.A.: 1991, “Interacting Localized Structures with Galilean Invariance,” Physical Review A: General Physics A44, 1110.Google Scholar
Glendinning, P. and Tresser, C.: 1985, “Heteroclinic loops leading to hyperchaos,” Phys. Lett. A46, 347.Google Scholar
Gilmore, R.: 1981, Catastrophe Theory for Scientists and Engineers, (Wiley and Sons, New York).Google Scholar
Moore, D.W. and Spiegel, E.A.: 1966, “A Thermally Excited Nonlinear Oscillator,” Astrophysical Journal 143, 871.Google Scholar
Spiegel, E.A.: 1972. “Convection in Stars. II. Special Effects,” Annual Review of Astronomy and Astrophysics 10, 261.Google Scholar
Spiegel, E.A.: 1985, “Cosmic Arrhythmias,” in Chaotic Behavior in Astrophysics, eds. Buchler, R., Perdang, J. and Spiegel, E.A. (Reidel, Dordrecht), p. 91.Google Scholar
Tresser, C.: 1984, “Homoclinic orbits for flows in R3 ,” J. Physique 45, 837.Google Scholar