A model oscillator of irregular stellar variability

We have studied a set of equations with nonlinear and nonadiabatic terms which describes a simple oscillator. The equations have only one fixed point located at the origin. It is found that the oscillator shows the sequence of the period-doubling for the change of a parameter and results in chaotic oscillation. We illustrated the behaviour of the oscillator for several set of parameters and showed that the equations of the oscillator can be reduced to the one-zone model of stellar pulsation with simple nonlinear terms. It is suggested that the stellar irregular variability is resulted from the chaotic motion due to the nonlinear effect.