Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
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In this paper, the stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force.About:
This article is published in Physics Letters A.The article was published on 1992-11-23. It has received 2957 citations till now. The article focuses on the topics: Control of chaos & System dynamics.read more
Citations
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Chaotic Responses in a Stable Duffing System of Non-ideal Type
TL;DR: In this article, the dynamics of a non-linear system with non-ideal excitation is studied and the existence of the Sommerfeld effect in such nonlinear nonidealy excited system is proved.
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Adaptive Sliding Mode Vibration Control of a Nonlinear Smart Beam: A Comparison with Self-Tuning Ziegler-Nichols PID Controller
Atta Oveisi,Mohammad Gudarzi +1 more
TL;DR: In this paper, a robust adaptive fuzzy control algorithm for controlling the proposed mechanical structure is introduced, which includes a fuzzy scheme and a robust controller based on sliding mode controller a fuzzy system is introduced to mimic an ideal controller, the robust controller is designed based on compensation of the difference between the fuzzy controller and the ideal controller.
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On Inverse Generalized Synchronization of Continuous Chaotic Dynamical Systems
Adel Ouannas,Zaid Odibat +1 more
TL;DR: In this article, the inverse generalized synchronization problem for different dimensional chaotic dynamical systems in continuous-time is proposed and investigated, and new results are derived using new control method and stability theory.
Journal ArticleDOI
Microcantilever chaotic motion suppression in tapping mode atomic force microscope
TL;DR: In this paper, the tapping mode atomic force microscopy is modeled and chaotic motion is identified for a wide range of the parameter's values and two control techniques are implemented: the optimal linear feedback control and the time-delayed feedback control.
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The optimal form of the fractional-order difference feedbacks in enhancing the stability of a sdof vibration system
Z.H. Wang,Y.G. Zheng +1 more
TL;DR: In this article, the concept of fractional-order difference feedback that generalizes the displacement difference feedback, velocity difference feedback and acceleration difference feedback is proposed for improving the stability of a vibration system.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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Synchronization in chaotic systems
TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
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An equation for continuous chaos
TL;DR: A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable as mentioned in this paper, which allows for a "folded" Poincare map (horseshoe map).
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Driving systems with chaotic signals.
TL;DR: It is shown that driving with chaotic signals can be done in a robust fashion, rather insensitive to changes in system parameters, and the calculation of the stability criteria leads naturally to an estimate for the convergence of the driven system to its stable state.
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Experimental control of chaos.
TL;DR: It was demonstrated that one can convert the motion of a chaotic dynamical system to periodic motion by controlling the system about one of the many unstable periodic orbits embedded in the chaotic attractor, through only small time dependent perturbations in an accessible system parameter.