Using small perturbations to control chaos

The extreme sensitivity of chaotic systems to tiny perturbations (the ‘butterfly effect’) can be used both to stabilize regular dynamic behaviours and to direct chaotic trajectories rapidly to a desired state. Incorporating chaos deliberately into practical systems therefore offers the possibility of achieving greater flexibility in their performance.

[1]  Dressler,et al.  Controlling chaos using time delay coordinates. , 1992, Physical review letters.

[2]  Alberto Tesi,et al.  Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems , 1992, Autom..

[3]  Grebogi,et al.  Unstable periodic orbits and the dimensions of multifractal chaotic attractors. , 1988, Physical review. A, General physics.

[4]  S. Sinha,et al.  Adaptive control in nonlinear dynamics , 1990 .

[5]  Grebogi,et al.  Experimental observation of crisis-induced intermittency and its critical exponent. , 1989, Physical review letters.

[6]  Singer,et al.  Controlling a chaotic system. , 1991, Physical review letters.

[7]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[8]  B. Huberman,et al.  Dynamics of adaptive systems , 1990 .

[9]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[10]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[11]  Goldhirsch,et al.  Taming chaotic dynamics with weak periodic perturbations. , 1991, Physical review letters.

[12]  Valery Petrov,et al.  Controlling chaos in the Belousov—Zhabotinsky reaction , 1993, Nature.

[13]  Grebogi,et al.  Controlling chaos in high dimensional systems. , 1992, Physical review letters.

[14]  Katsuhiko Ogata,et al.  Modern Control Engineering , 1970 .

[15]  Jerrold E. Marsden,et al.  Controlling homoclinic orbits , 1989 .

[16]  Brun,et al.  Control of NMR-laser chaos in high-dimensional embedding space. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  T. B. Fowler,et al.  Application of stochastic control techniques to chaotic nonlinear systems , 1989 .

[18]  L. Pecora,et al.  Tracking unstable orbits in experiments. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[19]  Mehta,et al.  Controlling chaos to generate aperiodic orbits. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[20]  Hamann,et al.  Transition from chaotic to nonchaotic behavior in randomly driven systems. , 1992, Physical review letters.

[21]  Lima,et al.  Suppression of chaos by resonant parametric perturbations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[22]  L. Wolfersdorf.  Potential Flow Past a Circular Cylinder with Permeable Surface , 1988 .

[23]  Azevedo,et al.  Controlling chaos in spin-wave instabilities. , 1991, Physical review letters.

[24]  Hua O. Wang,et al.  Robust Control of a Chaotic Dynamical System , 1992, 1992 American Control Conference.

[25]  Ditto,et al.  Experimental control of chaos. , 1990, Physical review letters.

[26]  Roy,et al.  Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. , 1992, Physical review letters.

[27]  Auerbach,et al.  Exploring chaotic motion through periodic orbits. , 1987, Physical review letters.

[28]  E. A. Jackson,et al.  Periodic entrainment of chaotic logistic map dynamics , 1990 .

[29]  E. Atlee Jackson,et al.  The entrainment and migration controls of multiple-attractor systems , 1990 .

[30]  Grebogi,et al.  Using the sensitive dependence of chaos (the "butterfly effect") to direct trajectories in an experimental chaotic system. , 1992, Physical review letters.

[31]  Roy,et al.  Tracking unstable steady states: Extending the stability regime of a multimode laser system. , 1992, Physical review letters.

[32]  Grebogi,et al.  Using chaos to direct orbits to targets in systems describable by a one-dimensional map. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[33]  Jackson Ea,et al.  Controls of dynamic flows with attractors. , 1991 .

[34]  Hübler,et al.  Nonlinear resonances and suppression of chaos in the rf-biased Josephson junction. , 1990, Physical review letters.

[35]  T. Vincent,et al.  Control of a chaotic system , 1991 .

[36]  A Garfinkel,et al.  Controlling cardiac chaos. , 1992, Science.

[37]  James A. Yorke,et al.  Lorenz-like chaos in a partial differential equation for a heated fluid loop , 1987 .

[38]  Freeman J. Dyson,et al.  Infinite in All Directions , 1988 .

[39]  Glorieux,et al.  Stabilization and characterization of unstable steady states in a laser. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[40]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[41]  Grebogi,et al.  Using chaos to direct trajectories to targets. , 1990, Physical review letters.

[42]  E. Hunt.  Stabilizing high-period orbits in a chaotic system: The diode resonator. , 1991 .

[43]  E. Ott,et al.  Controlling Chaotic Dynamical Systems , 1991, 1991 American Control Conference.

[44]  Grebogi,et al.  Communicating with chaos. , 1993, Physical review letters.

[45]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[46]  Celso Grebogi,et al.  Using chaos to target stationary states of flows , 1992 .