ResourceLetter CC1 Controlling Chaos Duke University资源信CC1混沌控制杜克大学.docVIP

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ResourceLetter CC1 Controlling Chaos Duke University资源信CC1混沌控制杜克大学.doc

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ResourceLetter CC1 Controlling Chaos Duke University资源信CC1混沌控制杜克大学

Resource Letter CC-1: Controlling Chaos Daniel J. Gauthier Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708 Abstract This Resource Letter provides a guide to the literature on controlling chaos. Journal articles, books, and web pages are provided for the following: controlling chaos, controlling chaos with weak periodic perturbations, controlling chaos in electronic circuits, controlling spatiotemporal chaos, targeting trajectories of nonlinear dynamical systems, synchronizing chaos, communicating with chaos, applications of chaos control in physical systems, and applications of chaos control in biological systems. I. Introduction Nonlinear systems are fascinating because seemingly simple “textbook” devices, such as a strongly-driven damped pendulum, can show exceedingly erratic, noise-like behavior that is a manifestation of deterministic chaos. Deterministic refers to the idea that the future behavior of the system can be predicted using a mathematical model that does not include random or stochastic influences. Chaos refers to idea that the system displays extreme sensitivity to initial conditions so that arbitrary small errors in measuring the initial state of the system grow large exponentially and hence practical, long-term predictability of the future state of the system is lost (often called the “butterfly effect”). Early nonlinear dynamics research in the 1980s focused on identifying systems that display chaos, developing mathematical models to describe them, developing new nonlinear statistical methods for characterizing chaos, and identifying the way in which a nonlinear system goes from simple to chaotic behavior as a parameter is varied (the so-called “route to chaos”). One outcome of this research was the understanding that the behavior of nonlinear systems falls into just a few universal categories. For example, the route to chaos for a pendulum, a nonlinear electronic circuit