A terminal dynamics model of the heartbeat

Abstract

It is widely assumed that heartbeat dynamics are chaotic, although there has been no evidence confirming such an opinion, and some evidence to the contrary. Additionally, the deterministic assumptions of such dynamics cannot be demonstrated. An alternative model is presented based upon the notion of terminal dynamics, which can more faithfully represent key features of the heartbeat: namely, piecewise determinism, and singular points between beats, which allow for adaptability while maintaining stability.

Dynamics of the level of deterministic chaos associated with gastric electrical uncoupling in dogs

“…These results indicate that although the level of deterministic chaos in EGG, changes substantially with gastric electrical uncoupling, electrode distances, configurations, and possibly a variety of other deterministic and non-deterministic factors could influence dramatically this change, and therefore increased levels of uncoupling are not necessarily related to increased levels of chaos. Since the balance of external factors (deterministic vs non-deterministic) is generally unknown, exploration of nondeterministic (stochastic) chaos models might be an additional avenue for furore studies (ZBILUT et al, 1996).…”

“…Chaotic signals can be classified using deterministic (KUBIN, 1995), or stochastic (ZBILUT et al, 1996) models. Dynamically, deterministic chaos represents the sensitivity of deterministic or quasi-deterministic processes to disturbances introduced by imprecisely known initial conditions (KUBIN, 1995).…”

Recurrence Quantification Analysis in Molecular Dynamics

“…Determinism (DET) is the percentage of recurrent points that appear in sequence, forming diagonal line structures in the distance matrix. DET corresponds to the amount of patches of recurrent behavior in the studied series, that is, to portions of the state space in which the system resides for a time longer than expected by chance alone (see Refs. 22 and 23).…”

Recurrence quantification analysis as a tool for characterization of molecular dynamics simulations

“…DET = determinism, and is the percentage of recurrent points that appear in sequence, forming diagonal line structures in the distance matrix. DET corresponds to the amount of patches of recurrent behavior in the studied series, i.e., to portions of the state space in which the system resides for a time longer than expected by chance alone (see [27,28]). This is a crucial point: a recurrence can, in principle, be observed by chance whenever the system explores two nearby points of its state space.…”