We present a model of the cardiovascular system (CVS) based on a system of coupled oscillators. Using this
approach we can describe several complex physiological phenomena that can have a range of applications. For
instance, heart rate variability (HRV), can have a new deterministic explanation. The intrinsic dynamics of the
HRV is controlled by deterministic couplings between the physiological oscillators in our model and without
the need to introduce external noise as is commonly done. This new result provides potential applications not
only for physiological systems but also for the design of very precise electronic generators where the frequency
stability is crucial. Another important phenomenon is that of oscillation death. We show that in our CVS
model the mechanism leading to the quenching of the oscillations can be controlled, not only by the coupling
parameter, but by a more general scheme. In fact, we propose that a change in the relative current state
of the cardiovascular oscillators can lead to a cease of the oscillations without actually changing the strength
of the coupling among them. We performed real experiments using electronic oscillators and show them to
match the theoretical and numerical predictions. We discuss the relevance of the studied phenomena to real
cardiovascular systems regimes, including the explanation of certain pathologies, and the possible applications
in medical practice.
KEYWORDS: Stochastic processes, Dynamical systems, Complex systems, Signal to noise ratio, Mathematical modeling, Interference (communication), Chaos, Systems modeling, Information theory, Monte Carlo methods
There exist a common belief that random sequences are produced
from very complicated phenomena, making impossible the construction of accurate mathematical models. It has been recently shown that under specific conditions the exact solutions to some chaotic functions can be generalized to produce truly random sequences. This establishes a transition from chaos to stochastic dynamics. Using this result we can obtain explicit output expressions for stochastic dynamics problems like those posed by stochastic resonant nonlinear systems. We show that in this kind of systems the phenomenon of noise-induced disorder-order can be more efficiently described with an information-theory approach through the determination of a parameter that measures the complexity of the dynamics. The Stochastic Resonance (SR) is just an example of the principal phenomenon wherein the complex stochastic dynamics is converted into a simpler one. Then we show the opposite phenomenon whereby the autonomous (without input noise) transition from chaotic order to stochastic disorder is achieved by a static non-invertible non-linearity. We build electronic systems to simulate and produce experimentally all these phenomena.
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