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The Model-Oscillators of Stellar Pulsation

  • Chapter
Stellar Pulsation — Nonlinear Studies

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 257))

Abstract

The recent works on the model-oscillators of stellar pulsation in relation to the nonlinear dynamics are reviewed. We first summarize nonlinear equations with nonlinear terms which cause irregular and chaotic oscillations. The Lorenz equation and its family are described. One of them, the Moore and Spiegel equation is mentioned as one of the simplest dissipative chaotic jerk equations. One-zone models not only for pulsation but also for convection are roughly reviewed. Nonlinearly coupled modal oscillations are explained by using coefficients of mode coupling for a standard model of stars. Bifurcation of phase-locking between modes of oscillation is demonstrated. The Farey tree and triangle are also explained. Then, the pulsation of a convective zone is outlined by using the parameter of convection in the stellar structure. Finally, we emphasize the interaction of multi-zones. It is suggested spatiotemporal behaviour should be studied, because a simple coupled map lattice shows chaotic phenomena such as the period doubling occurs not only in time but in space.

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Authors and Affiliations

  1. Faculty of Education, Ibaraki University, Mito, 310-8512, Japan

    Yasuo Tanaka

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  1. Yasuo Tanaka
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Editors and Affiliations

  1. Tohoku University, Japan

    Mine Takeuti

  2. Harvard University, USA

    Dimitar D. Sasselov

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Tanaka, Y. (2001). The Model-Oscillators of Stellar Pulsation. In: Takeuti, M., Sasselov, D.D. (eds) Stellar Pulsation — Nonlinear Studies. Astrophysics and Space Science Library, vol 257. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9698-5_6

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  • DOI: https://doi.org/10.1007/978-94-015-9698-5_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5653-5

  • Online ISBN: 978-94-015-9698-5

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