  The dynamical characterization of the heart rate is definitely a problem of
vital importance. The selection, construction and adjustment of models that
reproduce the dynamic behavior of the cardiac muscle, brings us closer to the
solution of the usual classification problem in medicine, i.e. decide whether
or not a patient belongs to the healthy class of patients. An usual model for
this dynamic is often given by a modified Van der Pol model (vdPM), whose
parameters are currently optimized with machine learning techniques or
evolutionary algorithms. In any of these cases, the proper selection of the
initial condition of the parameters drastically reduces the computational cost
of the optimization method used. In this work, a strategy to estimate a
positively invariant region that contains the periodic orbit, associated with a
set of particular parameters of the vdPM considered, is presented. An algorithm
is proposed to build the positively invariant region, the numerical results
confirm that the vdPM solutions starting within the positively invariant region
converge to the periodic orbit. This kind of result allows to reduce the cost
of searching for the optimal parameters that represent a real
electrocardiographic signal, which in turn, let us reduce the dimensionality of
the system allowing the design of more efficient classifiers for these signals.
