Characterization and control of laser chaos using unstable periodic orbits

2002 ◽  
Author(s):  
M. Lefranc ◽  
S. Bielawski ◽  
D. Derozier ◽  
P. Glorieux
Keyword(s):  
Periodic Orbits ◽  
Unstable Periodic Orbits ◽  
And Control

scholarly journals Computing and Controlling Basins of Attraction in Multistability Scenarios

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
John Alexander Taborda ◽  
Fabiola Angulo
Keyword(s):  
Fixed Point ◽  
Periodic Orbit ◽  
Periodic Orbits ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Control Technique ◽  
Unstable Periodic Orbits ◽  
Control Effort ◽  
Coexistence Of Attractors ◽  
And Control

The aim of this paper is to describe and prove a new method to compute and control the basins of attraction in multistability scenarios and guarantee monostability condition. In particular, the basins of attraction are computed only using a submap, and the coexistence of periodic solutions is controlled through fixed-point inducting control technique, which has been successfully used until now to stabilize unstable periodic orbits. In this paper, however, fixed-point inducting control is used to modify the domains of attraction when there is coexistence of attractors. In order to apply the technique, the periodic orbit whose basin of attraction will be controlled must be computed. Therefore, the fixed-point inducting control is used to stabilize one of the periodic orbits and enhance its basin of attraction. Then, using information provided by the unstable periodic orbits and basins of attractions, the minimum control effort to stabilize the target periodic orbit in all desired ranges is computed. The applicability of the proposed tools is illustrated through two different coupled logistic maps.

scholarly journals A SIMPLE APPROACH TO CALCULATION AND CONTROL OF UNSTABLE PERIODIC ORBITS IN CHAOTIC PIECEWISE-LINEAR SYSTEMS

2001 ◽  
Vol 11 (01) ◽  
pp. 215-224 ◽  
Author(s):  
TETSUSHI UETA ◽  
GUANRONG CHEN ◽  
TOHRU KAWABE
Keyword(s):  
Periodic Orbits ◽  
State Feedback ◽  
Piecewise Linear ◽  
Autonomous Systems ◽  
Simple Approach ◽  
State Feedback Control ◽  
Unstable Periodic Orbits ◽  
Simple Method ◽  
Controlled System ◽  
And Control

This paper describes a simple method for calculating unstable periodic orbits (UPOs) and their control in piecewise-linear autonomous systems. The algorithm can be used to obtain any desired UPO embedded in a chaotic attractor, and the UPO can be stabilized by a simple state feedback control. A brief stability analysis of the controlled system is also given.

APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM III: PREDICTABILITY AND CONTROL OF CHAOTIC MOTION

1994 ◽  
Vol 04 (04) ◽  
pp. 773-784 ◽  
Author(s):  
B. HÜBINGER ◽  
R. DOERNER ◽  
H. HENG ◽  
W. MARTIENSSEN
Keyword(s):  
Periodic Orbits ◽  
Chaotic Motion ◽  
Invariant Manifolds ◽  
Control Method ◽  
Equations Of Motion ◽  
Unstable Periodic Orbits ◽  
Physical Measure ◽  
Control Scheme ◽  
Feedback Control Method ◽  
And Control

We apply the concepts of predictability and control of chaotic motion to the driven damped pendulum. A physical measure of predictability is defined and determined from experimental data as well as from the equations of motion. The results are presented in predictability portraits which constitute an intrinsic pattern of zones of varying predictability. The origin of these patterns is related to the unstable periodic orbits and their invariant manifolds within the attractor. In order to control the chaotic motion of the pendulum we implement an extension of the OGY feedback control method, which we call “local control method.” With this control scheme any motion of the pendulum which is a solution of the systems equations of motion can be stabilized. We apply the control formalism in order to stabilize experimentally unstable periodic orbits as well as arbitrarily chosen chaotic trajectories.

On the Potential for Entangled States Between Chaotic Systems

2014 ◽  
Vol 24 (06) ◽  
pp. 1450077 ◽  
Author(s):  
Matthew A. Morena ◽  
Kevin M. Short
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Chaotic Systems ◽  
Entangled States ◽  
Future Research ◽  
Unstable Periodic Orbits ◽  
Qualitative Information ◽  
Chaotic Dynamical System ◽  
Naturally Occurring ◽  
External Intervention

We report on the tendency of chaotic systems to be controlled onto their unstable periodic orbits in such a way that these orbits are stabilized. The resulting orbits are known as cupolets and collectively provide a rich source of qualitative information on the associated chaotic dynamical system. We show that pairs of interacting cupolets may be induced into a state of mutually sustained stabilization that requires no external intervention in order to be maintained and is thus considered bound or entangled. A number of properties of this sort of entanglement are discussed. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. Based on certain properties of chaotic systems and on examples which we present, there is further potential for chaotic entanglement to be naturally occurring. A discussion of this and of the implications of chaotic entanglement in future research investigations is also presented.

scholarly journals Finding unstable periodic orbits: A hybrid approach with polynomial optimization

2021 ◽  
Vol 427 ◽  
pp. 133009
Author(s):  
Mayur V. Lakshmi ◽  
Giovanni Fantuzzi ◽  
Sergei I. Chernyshenko ◽  
Davide Lasagna
Keyword(s):  
Periodic Orbits ◽  
Polynomial Optimization ◽  
Hybrid Approach ◽  
Unstable Periodic Orbits

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

Sign in / Sign up

Export Citation Format

Share Document