  Some Miras -- long-period variables in late evolutionary stages -- have
meandering pulsation periods and light curve asymmetries, the causes of which
are still unclear. We aim to understand better the origin of these phenomena by
investigating a sample of solar-neighbourhood Miras. We characterised this
group of stars and related their variability characteristics to other stellar
parameters. We analysed observations from several databases to obtain light
curves with maximum time span and temporal coverage for a sample of 548 Miras.
We determined their pulsation period evolution over a time span of many
decades, searched for changes in the periods, and determined the amplitude of
the period change. We also analysed the Fourier spectra with respect to
possible secondary frequency maxima. The sample was divided into two groups
with respect to the presence of light curve bumps. IR colours and indicators of
the third dredge-up were collected to study the sample stars' mass-loss and
deep mixing properties. Our analysis revealed one new star, T~Lyn, with a
continuously changing period. The group of Miras with meandering period changes
is exclusively made up of M-type stars. The Fourier spectra of the meandering
period Miras have no prominent additional peaks, suggesting that additional
pulsation modes are not the cause of the meandering periods. We confirm that
bumps are more common among S and C Miras and show, for the first time, that
Miras with bumps have lower mass-loss rates than those with regular, symmetric
light curves. Also Miras with meandering period changes have relatively little
mass loss. We conclude that Miras with strongly changing periods or asymmetries
in their light curves have relatively low dust mass-loss rates. Meandering
period changes and light curve asymmetries could be connected to He-shell
flashes and third dredge-up episodes.
