  A new approach called Flow Curvature Method has been recently developed in a
book entitled Differential Geometry Applied to Dynamical Systems. It consists
in considering the trajectory curve, integral of any n-dimensional dynamical
system as a curve in Euclidean n-space that enables to analytically compute the
curvature of the trajectory - or the flow. Hence, it has been stated on the one
hand that the location of the points where the curvature of the flow vanishes
defines a manifold called flow curvature manifold and on the other hand that
such a manifold associated with any n-dimensional dynamical system directly
provides its slow manifold analytical equation the invariance of which has been
proved according to Darboux theory. The Flow Curvature Method has been already
applied to many types of autonomous dynamical systems either singularly
perturbed such as Van der Pol Model, FitzHugh-Nagumo Model, Chua's Model, ...)
or non-singularly perturbed such as Pikovskii-Rabinovich-Trakhtengerts Model,
Rikitake Model, Lorenz Model,... More- over, it has been also applied to
non-autonomous dynamical systems such as the Forced Van der Pol Model. In this
article it will be used for the first time to analytically compute the slow
invariant manifold analytical equation of the four-dimensional Unforced and
Forced Heartbeat Model. Its slow invariant manifold equation which can be
considered as a "state equation" linking all variables could then be used in
heart prediction and control according to the strong correspondence between the
model and the physiological cardiovascular system behavior.
