  Heart rate variability (HRV) series reflects the dynamical variation of
heartbeat-to-heartbeat intervals in time and is one of the outputs of the
cardiovascular system. Over the years, this system has been recognized for
generating nonlinear and complex heartbeat dynamics, with the latter referring
to a high sensitivity to small -- theoretically infinitesimal -- input changes.
While early research associated chaotic behavior with the cardiovascular
system, evidence of stochastic inputs to the system, i.e., a physiological
noise, invalidated those conclusions. To date, a comprehensive characterization
of the cardiovascular system dynamics, accounting for dynamical noise input,
has not been undertaken. In this study, we propose a novel methodological
framework for evaluating the presence of regular or chaotic dynamics in noisy
dynamical systems. The method relies on the estimation of asymptotic growth
rate of noisy mean square displacement series in a two-dimensional phase space.
We validated the proposed method using synthetic series comprising well-known
regular and chaotic maps. We applied the method to real HRV series from healthy
subjects, as well as patients with atrial fibrillation and congestive heart
failure, during unstructured long-term activity. Results indicate that HRV
series are consistently generated by a regular system driven by dynamical
noise.
