Recently developed techniques from nonlinear dynamical systems theory were applied to experiments on three physical nonlinear oscillators:​ the impacting pendulum;​ the spring pendulum;​ and, most extensively, the mammalian heart. The common goal among the sections of this dissertation is a quantitative description of the unstable or aperiodic behavior of a strongly nonlinear system.

The periodically forced impacting pendulum is a “piecewise nonlinear” system;​ its dynamics are defined by a sharp change in stiffness when the pendulum bob contacts a rigid stop. The experiments described in this dissertation clearly characterize subharmonic and chaotic oscillations in a physical impact oscillator. Experimental results were analyzed using Fourier power spectra, Poincare sections, time-delay embedding, and a fractal dimension algorithm. Instability near a period-doubling bifurcation was explored in depth using ideas from Floquet theory.

The spring pendulum is a 2-degree-of-freedom (2-DOF) nonlinear oscillator. It consists of a pendulum whose bob is allowed to slide radially, subject to the restoring force of a linear spring. Radial excitation of the elastic pendulum can lead to coupled, subharmonic, swinging motion. The stability of coupled, as well as purely radial, motion of the experimental spring-pendulum was measured using Floquet theory and the local geometry of transients in 4-dimensional state space.

Speculation about the relationship between ventricular fibrillation (VF) and chaos has been abundant, but attem pts to characterize the arrhythm ia have been hampered by poor data. Extensive amounts of high-quality data, consisting of electrograms sampled in time and space from the surface of animal hearts in fibrillation, were made available from experiments in Duke University’s Basic Arrhythm ia Lab. Power spectra, temporal and spatial correlation functions, fractal dimension estimates, and an orthogonal modal decomposition were extracted from the data. The degree of disorder in VF was quantified in several ways. These analyses indicate that VF involves a finite (< 500), but not small (> 6) number of degrees of freedom, suggesting that low-dimensional chaos is not responsible for its complexity.