Stellar pulsation is one of the condidates for strong mass loss from red giant stars. Recent investigations have shown sporadic outbursts of the pulsation can eject a considerable mass from the stars. Such a sporadic increase of the amplitudes seems to have a connection with the irregularity found in the pulsations. Recently the iregular propreties in stellar pulsation are investigated in the relation to nonlinear dynamics (see for instance Perdang, 1985). Unfortunately no single model oscillator of a star of which the equilibrium state is dynamically stable had been found. In the present paper, we shall discuss a simple oscillator which shows period-doubling and chaotic, that is, irregular oscillations.