Weak chaos in long-period variables.

In order to account for the increasing irregularity of the long-period variations of low- to intermediate-mass stars, ways in which the outer layers of an evolved AGB star respond to pulsations which originate in the stellar interior are investigated. It is assumed that the oscillations arise in a zone of instability well below the stellar photosphere. The star's mantle is driven periodically by pressure waves generated by the interior motion. This type of driven oscillator exhibits chaotic motions for a wide range of relevant parameters. Analytic estimates show why and where chaos should set in; extensive numerical experiments confirm and extend these findings. Motions are regularly periodic at first, then become multiperiodic, and finally chaotic, while the mass of the mantle decreases more and more rapidly through mass loss.