Using the Sensitive Dependence of Chaos (the "Butterfly Effect") to Direct Trajectories in an Experimental Chaotic System Troy Shinbrot, ' ' " ' William Ditto Celso Grebogi, ' ' " ' ' Edward Ott Mark Spano, and James A. Yorke '~ ' "iUniversity of Maryland. College Park, Maryland 20742 Department of Physics, The College of Wooster, Wooster, Ohio 4469l IVaval Surface Warfare Center. Silver Spring...

The long-term unprcdictability associated with chaos may be undesirable in certain settings. Ott, Grebogi, and Yorke (Phys. Rev. Lett. 1990.64, 1196) have recently proposed a method by which any of the infinite number of unstable periodic orbits embedded within a strange attractor can be, in principle, stabilized through small, controlled perturbations of a system constraint. This method is app...

Background Recently, development of chaos theory brings up scientist into a new era in analyzing nonlinear systems. It is known that the chaos exhibits a deterministic random behavior. In particular, the OGY (OttGrebogi-Yorke) method drove the research of chaos control to nonlinear analyst. Yet it needs more investigation on such nonlinear systems in designing control algorithms. Recently, Vinc...

An approach is proposed for making chaotic a given stable Takagi–Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mec...

In this paper, a buck-boost dc/dc converter under a typical current-mode control is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of the one-sided shift map, which implies positive entropy of the system and hence chaotic behavior. The essential tool is the horseshoe hypotheses propos...

An analysis of experimental data from the RFX (Reversed Field eXperiment) reversed field pinch machine [L.sion Eng. Des. 25, 315 (1995)] is carried out to investigate the possible existence of deterministic chaos in the edge plasma region. The mathematical tools used include Lyapunov exponents, Kaplan–Yorke dimension, minimum embedding dimension estimates and nonlinear forecasting. The whole an...

We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method...

In this paper, a mathematical analysis of a possible way to chaos (in the sense of Li and Yorke) for bounded piecewise smooth systems of dimension three submitted to nonsmooth transitions is proposed. This study is based on period doubling method applied to the relied Poincaré map defined on a Poincaré section chosen in the neighborhood of the bifurcation point and transverse to the switching m...

This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from 2.0 to 3.0 by a single control parameter. Such a parameter provides a means to explore the route through limit cycles, period-doubling, dissipative chaos, and eventually conservative chaos. With an absolute-value nonlinearity and certain choices of parameters, ...