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Discrete Map Simulation of Stellar Oscillations

  • J. Perdang
Chapter
Part of the NATO ASI Series book series (ASIC, volume 302)

Abstract

In order to isolate the classes of nonlinear mono-mode stellar oscillations, we introduce a simulation of the pulsation dynamics by a parametrized iterative algebraic map whose structure is derived from the equations of stellar fluid dynamics. We report here on an extensive numerical investigation of the rôle of 3 of the parameters of the map. Among the latter the linear growth-rate times the linear period is found to play a dominant part: Under well specified conditions this parameter generates a Feigenbaum period-doubling sequence. We further show that the 3-dimensional free parameter space supports period-K oscillations, K any integer. While P-1, P-2, P-4 and P-8 oscillations occupy most of the parameter space over which the oscillations are regular, P-3 and P-6 as well as P-5 and P-7 oscillations are carried by smaller zones. Our numerical results are also indicative that the regular region in the parameter space is crisscrossed by a web of chaotic behaviour. A numerical investigation of the geometry of the region in the 3-dimensional free parameter space sustaining regular oscillations indicates that the boundary of this zone has a locally irregular fractal-like structure which alternates with an apparently smooth structure. We argue that this result implies that the zone of regular oscillations in the HR-diagram shows a fractal-like boundary in some regions while in other parts of the HR-diagram this boundary is smooth. Accordingly an evolutionary track of a star will cut the boundary of regular behaviour a large number of times if the crossing occurs near a locally fractal-like stretch. Our iterative model is thus consistent with the observation of a variety of transitions from regular oscillations to chaos and from chaotic oscillations back to regular behaviour in variable stars.

Keywords

Chaotic Oscillation Variable Star Control Space Random Initial Condition Regular Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • J. Perdang
    • 1
  1. 1.Institute of AstronomyCambridgeUK

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