## Applied chaosSince its inception, the science of chaos has caused excitement and activity in theoretical circles as far apart as physics and economics, and in disciplines ranging from mathematics to ecology. Its central revelation - that even a simple deterministic system can yield complex behavior such as chaos - suggests a glimmer of hope that the salient features of complex problems might be captured, even understood, in terms of simple models and the paradigm of chaos. Conventional analysis can explain numerous phenomena. Yet many dynamic systems remain mysteries to which chaos may hold a crucial key. To explore this possibility in the context of applications, the Electric Power Research Institute recently sponsored the International Workshop on Applications of Chaos. This fascinating book is the result. At EPRI's invitation, a group of physicists, chemists, mathematicians, engineers of every variety, as well as physiologists, computer scientists, and others came together from all over the globe to speak about and discuss the applications of chaos. The twenty papers presented included such topics as Global Integrity in Engineering Dynamics, Atmospheric Flight Dynamics and Chaos, New Applications of Chaos in Chemical Engineering, Controlling the Dynamics of Chaotic Convective Flows, Real-Time Identification of Flame Dynamics, and Applications of Chaos to Physiology and Medicine. The scope of their discussion illustrates both the interdisciplinary nature of chaotic dynamics and the wide variety of applications, from engineering to cardiology. It is also clear from the results that chaotic dynamics is pervasive and will be of increasing importance in many areas of applied science and technology.Applied Chaos represents the next generation of technology in its infancy, a hint of the enormous possibilities that might be found in the practical applications of this new science. |

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### Contents

BRIDGING THE GAP BETWEEN THE SCIENCE OF CHAOS | 3 |

GLOBAL INTEGRITY IN ENGINEERING DYNAMICS | 31 |

DYNAMIC INSTABILITIES AND CHAOS IN RUNNING BELTS | 51 |

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aerodynamic amplitude analysis applications approximation basin boundary belt bifurcation diagram cardiac chaos chaotic advection chaotic attractor chaotic behavior chaotic dynamics chaotic responses chaotic saddle complex computed convection correlation Cvitanovic cycle expansions data points data set deterministic dimension discussed Doming dynamical systems ectopic eigenvalues engineering systems example experimental fixed point flame flight dynamic flow fluid forcing forecasting fractal frequency global Gorman heart rate heat transfer homoclinic increases initial conditions iterated limit cycle linear Lorenz equations low-dimensional Lyapunov exponents measure mechanical methods mode motion noise nonlinear dynamics nonlinear model number of data observed oscillations parameter parasystole period-doubling periodic orbit perturbation phase space Phys plot Poincare power spectra prediction premixed flame probability density problem reactors reconstruction reference spheres region resonance saddle-node bifurcation sequence shown in Figure shows simple sinus stable stochastic strange attractor structure techniques tion trajectories transient unstable manifold values variability velocity vibration