Classical harmonic three-body system: an experimental electronic realization.

The classical three-body harmonic system in [Formula: see text] ([Formula: see text]) with finite rest lengths and zero total angular momentum [Formula: see text] is considered. This model describes the dynamics of the [Formula: see text] near-equilibrium configurations of three point masses [Formula: see text] with arbitrary pairwise potential [Formula: see text] that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the intrinsic parameters and initial states of the system are independently set by voltage inputs. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment.

Generation of ECG signals from a reaction-diffusion model spatially discretized.

We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is shown that under ventricular fibrillation, the electrocardiogram signal is chaotic and the transition from sinus rhythm to chaos is consistent with the Ruelle-Takens-Newhouse route to chaos, as experimental studies indicate. The proposed model constitutes a useful tool for research, medical education, and clinical testing purposes. An electronic device based on the model was built for these purposes.

Periodically kicked network of RLC oscillators to produce ECG signals.

We propose a simple model of the electrical activity of the heart that reproduces realistic healthy electrocardiogram (ECG) signals. The model consists of two RLC linear oscillators periodically kicked by impulses of the main pacemaker with the frequency rate of a real heart. In the proposed model, one oscillator represents the atria, another represents the ventricles, and an electrical cardiac conduction system is included using a coupling capacitor, which can be either unidirectional or bidirectional. The network of the two capacitively coupled oscillators is periodically kicked by the main pacemaker to introduce the periodic forcing of limit cycles into the system; a time delay is introduced to represent the electrical transport delay from atria to ventricles. In this manner, healthy synthetic ECG signals are obtained by combining the signals of the currents of the oscillators. We show that an analytical solution of the model can be obtained when a single impulse is applied. From this, by the superposition principle, a solution with an impulse train is obtained. Note that analytical treatment is a feature not available in current cardiac oscillator models.