Journal ArticleDOI
Controlling chaotic dynamical systems
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In this paper, the authors describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1992-09-15. It has received 401 citations till now. The article focuses on the topics: Attractor & Crisis.read more
Citations
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The control of chaos: theory and applications
TL;DR: In this paper, the Ott-Grebogi-Yorke (OGY) method and the adaptive method for chaotic control are discussed. But the authors focus on the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions.
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Using small perturbations to control chaos
TL;DR: 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.
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An observer looks at synchronization
Henk Nijmeijer,Iven Mareels +1 more
TL;DR: The topic of synchronization of the response of systems has received considerable attention and this concept is revisited in the light of the classical notion of observers from (non)linear control theory.
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A unified approach to controlling chaos via an LMI-based fuzzy control system design
TL;DR: Simulation results show the utility of the unified design approach based on LMIs proposed in this paper, and the chaotic model following control problem, which is more difficult than the synchronization problem, is discussed using the EL technique.
References
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Journal ArticleDOI
A Two-dimensional Mapping with a Strange Attractor
TL;DR: In this article, the same properties can be observed in a simple mapping of the plane defined by: \({x i + 1}} = {y_i} + 1 - ax_i^2,{y i+ 1} = b{x_i}\).
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Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory
TL;DR: In this paper, a method for computing all of the Lyapunov characteristic exponents of order greater than one is presented, which is related to the increase of volumes of a dynamical system.
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Crises, sudden changes in chaotic attractors, and transient chaos
TL;DR: In this article, the authors show that crisis events are prevalent in many circumstances and systems, and that, just past a crisis, certain characteristic statistical behavior (whose type depends on the type of crisis) occurs.
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The dimension of chaotic attractors
TL;DR: In this paper, the authors discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors, and conclude that dimension of the natural measure is more important than the fractal dimension.