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Coupled-Oscillators

Published online by Cambridge University Press:  12 April 2016

Y. Tanaka
Y. Tanaka*
Affiliation:
Faculty of Education, Ibaraki University, Bunkyo, Mito 310, Japan

Abstract

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Modal coupling oscillation models for the stellar radial pulsation and coupled-oscillators are reviewed. Coupled-oscillators with the second-order and third-order terms seemed to behave non-systematically. Using the equation by Schwarzschild and Savedoff (1949) with the dissipation term of van del Pol’s type which is third-order, we demonstrate the effect of each term. The effects can be understood by the terms of the nonlinear dynamics, which is recently developing, that is. phase-locking, quasi-periodicity, period doubling, and chaos. As the problem of stellar pulsation, especially of double-mode cepheids on the period-ratio, we examine the dependence on the stellar structure from which the coupling constants in the second-order terms are derived. Eigen functions for adiabatic pulsations had been used for the calculation of the constants. It is noted that only two set of the constants are available, that is, for the polytrope model with n = 3 and a cepheid model without convection. Some examples of nonlinear dynamical effects will be shown.

It is shown that if the constants were suitable values, the period-ratio of double-mode cepheids is probably realized. The possibility is briefly suggested.

Type
III. Models
Information
International Astronomical Union Colloquium , Volume 134: Nonlinear Phenomena in Stellar Variability , 1993 , pp. 333 - 341
Copyright
Copyright © Kluwer 1993

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