  Delay differential equations (DDEs) are widely used in mathematical modeling
to describe physical and biological systems. Delays can impact model dynamics,
resulting in oscillatory behavior. In physiological systems, this instability
may signify (i) an attempt to return to homeostasis or (ii) system dysfunction.
In this study, we analyze a nonlinear, nonautonomous, nonhomogeneous open-loop
neurological control model describing the autonomic nervous system response to
the Valsalva maneuver. Unstable modes have been identified as a result of
parameter interactions between the sympathetic delay and time-scale. In a
two-parameter bifurcation analysis, we examine both the homogeneous and
nonhomogeneous systems. Discrepancies between solutions result from the
presence of the forcing functions which stabilize the system. We use analytical
methods to determine stability regions for the homogeneous system, identifying
transcendental relationships between the parameters. We also use computational
methods to determine stability regions for the nonhomogeneous system. The
presence of a Hopf bifurcation within the system is discussed and solution
types from the sink and stable focus regions are compared to two control
patients and a patient with postural orthostatic tachycardia syndrome (POTS).
The model and its analysis support the current clinical hypotheses that
patients suffering from POTS experience altered nervous system activity.
