Stabilizing the unstable periodic orbits of a chaotic system using adaptive time-delayed state feedback

This letter presents a new hyperchaotic system, which was constructed by adding an approximate time delayed state feedback to the second equation of Lorenz chaotic system. The constructed system is not only demonstrated by numerical simulations but also implemented via an electronic circuit, showing very good agreement with the simulation results.

Download Full-text

Stabilizing the unstable periodic orbits of a hybrid chaotic system using optimal control

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2014.06.026 ◽

2015 ◽

Vol 20 (3) ◽

pp. 1043-1056 ◽

Cited By ~ 10

Author(s):

Yosra Miladi ◽

Moez Feki ◽

Nabil Derbel

Keyword(s):

Optimal Control ◽

Periodic Orbits ◽

Chaotic System ◽

Unstable Periodic Orbits

Download Full-text

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

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127401002092 ◽

2001 ◽

Vol 11 (01) ◽

pp. 215-224 ◽

Cited By ~ 4

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.

Download Full-text

NEW METHOD FOR STABILIZATION OF UNSTABLE PERIODIC ORBITS IN CHAOTIC SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127495000247 ◽

1995 ◽

Vol 05 (01) ◽

pp. 281-295 ◽

Cited By ~ 11

Author(s):

ZBIGNIEW GALIAS

Keyword(s):

Periodic Orbits ◽

Chaotic System ◽

System Parameter ◽

Chaotic Systems ◽

New Method ◽

Unstable Periodic Orbits ◽

Numerical Example ◽

Element Set

In this paper we present a new method of controlling periodic orbits in chaotic systems. This method can be applied in situations when the chaotic system depends on one system parameter, which can be changed over a continuous interval or over a discrete, two-element set. We compare the new method to other ones, discuss its properties, and illustrate our approach with a numerical example.

Download Full-text

Tracking inherent periodic orbits in chaotic system via adaptive time delayed self-control

Proceedings of the 36th IEEE Conference on Decision and Control ◽

10.1109/cdc.1997.650656 ◽

2002 ◽

Cited By ~ 5

Author(s):

Xinghuo Yu

Keyword(s):

Periodic Orbits ◽

Chaotic System ◽

Self Control ◽

Adaptive Time

Download Full-text

Ubiquitous quantum scarring does not prevent ergodicity

Nature Communications ◽

10.1038/s41467-021-21123-5 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Saúl Pilatowsky-Cameo ◽

David Villaseñor ◽

Miguel A. Bastarrachea-Magnani ◽

Sergio Lerma-Hernández ◽

Lea F. Santos ◽

...

Keyword(s):

Phase Space ◽

Periodic Orbits ◽

Chaotic System ◽

Chaotic Regime ◽

Quantum States ◽

Unstable Periodic Orbits ◽

Quantum Ergodicity ◽

Long Time ◽

Dicke Model ◽

Random States

AbstractIn a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born’s rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.

Download Full-text