Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
Chaotic attractors in striped rectangular shapes generated by a Rössler-like system ☆
TL;DR: In this paper, the chaotic attractors are constructed by adding bounded and non-smooth feedback control to the Rossler system and the shape of a generated chaotic attractor can be adjusted by changing some control parameters.
Journal ArticleDOI
Analytical approximations for the periodic motion of the Duffing system with delayed feedback
Xiangcheng You,Hang Xu +1 more
TL;DR: The homotopy analysis method is developed to give periodic solutions of delayed differential equations that describe time-delayed position feedback on the Duffing system, finding that the current technique leads to higher accurate prediction on the local dynamics of time-Delayed systems near a Hopf bifurcation than the energy analysis method or the traditional method of multiple scales.
Journal ArticleDOI
Targeting in systems with discontinuities, with applications to power electronics
TL;DR: In this paper, the multivalued inverse function is used to generate multiple preimages of the target region which quickly cover the attractor, which is applied to the current-controlled boost converter in order to jump between two controlled states.
Journal ArticleDOI
Multistep method for controlling chaos
TL;DR: In this paper, a multistep control method where the trajectory on a chaotic attractor is directed by small perturbations towards a chosen fixed point is presented, giving a significant reduction of the chaotic transient preceding the controlled motion as compared with the Ott-Grebogi-Yorke method.
Journal ArticleDOI
Delayed feedback control of chaos in a switched arrival system
TL;DR: In this paper, a delayed impulsive feedback method is proposed for stabilizing unstable long periodic orbits embedded in the chaotic attractor, which does not rely on a priori knowledge of the position of the orbit to be stabilized.
References
More filters
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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).
Journal ArticleDOI
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.
Journal ArticleDOI
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.