Abstract
Up to now, the period-doubling bifurcation in variable star is identified through the existence of subharmonics in the power spectrum of light curves. Therefore the question is arisen: How to find a general criterion of period-doubling bifurcation in pulsating stars from theoretical analysis. It is discussed in this paper. We found that for the stellar pulsating mapping the bifurcation from a fixed point to a two-cycle occurs at parameter , i.e., adiabatic exponent .
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