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
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Chaos control in economical model by time-delayed feedback method
TL;DR: In this paper, a two-dimensional map describing chaotic behaviour of an economic model has been stabilized on various periodic orbits by the use of Pyragas time-delayed feedback control.
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Synchronization of chaotic systems with parametric uncertainty using active sliding mode control
TL;DR: An active sliding mode control method for synchronizing two chaotic systems with parametric uncertainty is presented, and a sufficient condition is drawn for the robust stability of the error dynamics and is applied to guiding the design of the controllers.
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Delayed feedback control of chaos by self-adapted delay time
TL;DR: In this paper, a continuous feedback loop is proposed for stabilizing unstable periodic orbits of chaotic systems, where the delay is chosen to be equal to the interval between the last and the k th previous maximum of the output signal.
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Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter
TL;DR: In this article, an adaptive control scheme for the synchronization of a unified chaotic system with an uncertain parameter is presented based on the Lyapunov stability theory, and the control performances are verified by numerical simulations.
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Regenerative memory in time-delayed neuromorphic photonic resonators
TL;DR: This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals.
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.