Coupled Oscillators
Abstract
Modal coupling oscillation models for the stellar radial pulsation and coupledoscillators are reviewed. Coupledoscillators with the secondorder and thirdorder terms seemed to behave nonsystematically. Using the equation by Schwarzschild and Savedoff (1949) with the dissipation term of van del Pol's type which is thirdorder, 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. phaselocking, quasiperiodicity, period doubling, and chaos. As the problem of stellar pulsation, especially of doublemode cepheids on the periodratio, we examine the dependence on the stellar structure from which the coupling constants in the secondorder 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 withn = 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 periodratio of doublemode cepheids is probably realized. The possibility is briefly suggested.
 Publication:

Astrophysics and Space Science
 Pub Date:
 December 1993
 DOI:
 10.1007/BF00657920
 Bibcode:
 1993Ap&SS.210..333T
 Keywords:

 Cepheid Variables;
 Coupled Modes;
 Oscillators;
 Stellar Oscillations;
 Chaos;
 Convective Flow;
 Period Doubling;
 Stellar Models;
 Astrophysics