Stabilizing unstable periodic orbits in higher dimensional systems based on stability transformation method

2012 ◽  
Author(s):  
Takumi Hasegawa ◽  
Tadashi Tsubone
Keyword(s):  
Periodic Orbits ◽  
Transformation Method ◽  
Unstable Periodic Orbits ◽  
Stability Transformation Method ◽  
Higher Dimensional

scholarly journals STABILIZATION OF UNSTABLE PERIODIC ORBITS FOR DISCRETE TIME CHAOTIC SYSTEMS BY USING PERIODIC FEEDBACK

2006 ◽  
Vol 16 (02) ◽  
pp. 311-323 ◽  
Author(s):  
ÖMER MORGÜL
Keyword(s):  
Periodic Orbits ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Unstable Periodic Orbits ◽  
Discrete Time Systems ◽  
Feedback Scheme ◽  
Higher Dimensional ◽  
Periodic Feedback ◽  
Time Systems ◽  
Stability Results

We propose a periodic feedback scheme for the stabilization of periodic orbits for discrete time chaotic systems. We first consider one-dimensional discrete time systems and obtain some stability results. Then we extend these results to higher dimensional discrete time systems. The proposed scheme is quite simple and we show that any hyperbolic periodic orbit can be stabilized with this scheme. We also present some simulation results.

Efficient switching between controlled unstable periodic orbits in higher dimensional chaotic systems

1995 ◽  
Vol 51 (5) ◽  
pp. 4169-4172 ◽  
Author(s):  
Ernest Barreto ◽  
Eric J. Kostelich ◽  
Celso Grebogi ◽  
Edward Ott ◽  
James A. Yorke
Keyword(s):  
Periodic Orbits ◽  
Chaotic Systems ◽  
Unstable Periodic Orbits ◽  
Higher Dimensional

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
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