Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

2003 ◽  
Vol 13 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Diego Pazó ◽  
Michael A. Zaks ◽  
Jürgen Kurths
Keyword(s):  
Periodic Orbits ◽  
Unstable Periodic Orbits ◽  
Lag Synchronization ◽  
Chaotic Oscillators

scholarly journals Intermittent chaos driven by nonlinear Alfvén waves

2004 ◽  
Vol 11 (5/6) ◽  
pp. 691-700 ◽  
Author(s):  
E. L. Rempel ◽  
A. C.-L. Chian ◽  
A. J. Preto ◽  
S. Stephany
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Systems Approach ◽  
Alfven Waves ◽  
Space Plasmas ◽  
Alfvén Waves ◽  
Unstable Periodic Orbits ◽  
Phase Dynamics ◽  
Intermittent Chaos

Abstract. We investigate the relevance of chaotic saddles and unstable periodic orbits at the onset of intermittent chaos in the phase dynamics of nonlinear Alfvén waves by using the Kuramoto-Sivashinsky (KS) equation as a model for phase dynamics. We focus on the role of nonattracting chaotic solutions of the KS equation, known as chaotic saddles, in the transition from weak chaos to strong chaos via an interior crisis and show how two of these unstable chaotic saddles can interact to produce the plasma intermittency observed in the strongly chaotic regimes. The dynamical systems approach discussed in this work can lead to a better understanding of the mechanisms responsible for the phenomena of intermittency in space plasmas.

scholarly journals Pattern recognition using chaotic neural networks

1998 ◽  
Vol 2 (4) ◽  
pp. 243-247 ◽  
Author(s):  
Z. Tan ◽  
B. S. Hepburn ◽  
C. Tucker ◽  
M. K. Ali
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Pattern Recognition ◽  
Dynamical Systems ◽  
Periodic Orbits ◽  
Basins Of Attraction ◽  
Limited Information ◽  
Unstable Periodic Orbits ◽  
Chaotic Neural Networks

Pattern recognition by chaotic neural networks is studied using a hyperchaotic neural network as model. Virtual basins of attraction are introduced around unstable periodic orbits which are then used as patterns. Search for periodic orbits in dynamical systems is treated as a process of pattern recognition. The role of synapses on patterns in chaotic networks is discussed. It is shown that distorted states having only limited information of the patterns are successfully recognized.

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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