SIMBAD references

We apply the global flow reconstruction method to the irregular pulsations of a W Virginis model that were computed with a state-of-the-art numerical hydrodynamical code and that were shown to be of a chaotic nature (Kovacs & Buchler 1988). It is shown that, even though the numerical hydrodynamics difference equations constitute a 180-dimensional `Phase-space', the complicated, irregular pulsational behavior of this stellar model is generated by a mere 3D map or flow that can be well approximated by a polynomial. The points in phase-space that are covered by the pulsations (i.e. the attractor) are shown to have a fractal dimension of ≃2.02. Furthermore, the minimum embedding dimension of the attractor is found to be 3. From these results we can conclude that the dimension of the effective physical phase-space is also 3, i.e. the light-curve, radial velocity curve or the behavior of any other variable, remarkably, can be obtained as the solution of a set of 3 first order ordinary differential equations. Previous theoretical results have already suggested that the onset of this chaos is correlated with a resonance of the fundamental mode with an overtone mode. The physical implications of our analysis will be that the dynamics of these models is governed by the interaction of just two vibrational modes.