Dynamical simulations of long-period variables calculated for greater
than 500 yr, i.e., longer than the typical thermal timescale for the s
tellar envelope, reveal clear and significant changes in the internal
energy (entropy) structure of the pulsating envelope. These changes ca
use the envelope to switch from a nearby steady pulsation in the first
harmonic overtone to stable pulsation in the fundamental mode. Howeve
r, as a result of the changes in the envelope's structure, the period
of this fundamental mode is significantly shorter than that predicted
for the initial, static envelope by linear mode analysis. Our major co
nclusion, derived from these simulations, is that the pulsation featur
e of LPVs, including their periods, cannot be predicted by the common
linear analysis but only by use of full, nonlinear hydrodynamic models
calculated for longer time intervals than has been the common practic
e.