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

2015 ◽  
Vol 20 (3) ◽  
pp. 1043-1056 ◽  
Author(s):  
Yosra Miladi ◽  
Moez Feki ◽  
Nabil Derbel
Keyword(s):  
Optimal Control ◽  
Periodic Orbits ◽  
Chaotic System ◽  
Unstable Periodic Orbits

Extended resonant feedback technique for controlling unstable periodic orbits of chaotic system

2009 ◽  
Vol 14 (12) ◽  
pp. 4273-4279 ◽  
Author(s):  
Arūnas Tamaševičius ◽  
Elena Tamaševičiūtė ◽  
Tatjana Pyragienė ◽  
Gytis Mykolaitis ◽  
Skaidra Bumelienė
Keyword(s):  
Periodic Orbits ◽  
Chaotic System ◽  
Unstable Periodic Orbits

Stabilization of unstable periodic orbits for a chaotic system

1999 ◽  
Vol 38 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Yang Genke ◽  
Wei Shuzhi ◽  
Wei Junhu ◽  
Zeng Jianchao ◽  
Wu Zhiming ◽  
...  
Keyword(s):  
Periodic Orbits ◽  
Chaotic System ◽  
Unstable Periodic Orbits

NEW METHOD FOR STABILIZATION OF UNSTABLE PERIODIC ORBITS IN CHAOTIC SYSTEMS

1995 ◽  
Vol 05 (01) ◽  
pp. 281-295 ◽  
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.

scholarly journals Ubiquitous quantum scarring does not prevent ergodicity

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.

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