  The intermittent on-off switching of feedback control is considered as a
major mechanism of postural stabilization during human quiet standing, which
can be modeled by switched-type hybrid stochastic delay differential equations
with unstable subsystems. Dynamics of the model can also be described by the
corresponding switched-type Fokker-Planck (FP) equations. Here, we develop a
comprehensive numerical recipe to simulate switched-type FP equations in the
case that the probability current is conserved at the switching boundary, as is
the case for noise-free models exhibiting C^0-continuity for solutions at the
boundary, but in a way extendable to cases with discontinuous jump.
Specifically, the FP equations are approximated by a finite state Markov chain
model using the finite element method. Then, dynamics of the Markov chain
model, including time evolution of probability density function (PDF),
stationary PDF, and power spectrum of postural sway are analyzed. We further
investigate how the stationary PDF alters as values of important parameters of
the model change. Dynamics of the Markov chain model are compared with Monte
Carlo-based dynamics of the model, by which the developed numerical recipe is
validated. The obtained Markov chain model forms a basis of our future
investigations of the intermittent postural control as a Markov decision
process.
