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.

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.

scholarly journals Concurrent effect of Alfvén waves and planar magnetic structure on geomagnetic storms

2019 ◽  
Vol 490 (3) ◽  
pp. 3440-3447 ◽  
Author(s):  
Zubair I Shaikh ◽  
Anil Raghav ◽  
Geeta Vichare ◽  
Ankush Bhaskar ◽  
Wageesh Mishra ◽  
...  
Keyword(s):  
Magnetic Structure ◽  
Geomagnetic Storms ◽  
Recovery Phase ◽  
Alfven Waves ◽  
Magnetic Clouds ◽  
Alfvén Waves ◽  
Fast Recovery ◽  
Interplanetary Coronal Mass Ejection ◽  
Mass Ejection

ABSTRACT Generally, interplanetary coronal mass ejection (ICME) triggers intense and strong geomagnetic storms. It has been established that the ICME sheath-moulded planar magnetic structure enhances the amplitude of the storms. Alfvén waves embedded in ICME magnetic clouds or high solar streams including corotating interacting regions (CIRs) in turn extend the recovery phase of the storm. Here, we investigate a geomagnetic storm with a very complex temporal profile with multiple decreasing and recovery phases. We examine the role of planar magnetic structure (PMS) and Alfvén waves in the various phases of the storm. We find that fast decrease and fast recovery phases are evident during transit of PMS regions, whereas a slight decrease or recovery is found during the transit of regions embedded with Alfvénic fluctuations.

Role of trapped and circulating particles in inducing current drive and radial electric field by Alfvén waves in tokamaks

2002 ◽  
Vol 67 (5) ◽  
pp. 301-308 ◽  
Author(s):  
V. S. TSYPIN ◽  
R. M. O. GALVÃO ◽  
I. C. NASCIMENTO ◽  
M. TENDLER ◽  
J. H. F. SEVERO ◽  
...  
Keyword(s):  
Electric Field ◽  
Radial Electric Field ◽  
Alfven Waves ◽  
Current Drive ◽  
Alfvén Waves ◽  
Trapped Particles ◽  
Transport Barriers

Absorption by trapped particles is supposed to seriously hinder current drive by Alfvén waves. However, it is shown in this paper that the same effect is rather beneficial for the emergence of the radial electric field induced by these waves, which is important for creating and maintaining transport barriers in tokamaks.

scholarly journals Feedback control modulation for controlling chaotic maps

2021 ◽  
Vol 26 (3) ◽  
pp. 419-439
Author(s):  
Roberta Hansen ◽  
Graciela A. González
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Periodic Orbits ◽  
Waiting Time ◽  
Control Parameter ◽  
Chaotic Maps ◽  
Noise Sensitivity ◽  
Control Methods ◽  
Unstable Periodic Orbits ◽  
Discrete Maps

Based on existing feedback control methods such as OGY and Pyragas, alternative new schemes are proposed for stabilization of unstable periodic orbits of chaotic and hyperchaotic dynamical systems by suitable modulation of a control parameter. Their performances are improved with respect to: (i) robustness, (ii) rate of convergences, (iii) reduction of waiting time, (iv) reduction of noise sensitivity. These features are analytically investigated, the achievements are rigorously proved and supported by numerical simulations. The proposed methods result successful for stabilizing unstable periodic orbits in some classical discrete maps like 1-D logistic and standard 2-D Hénon, but also in the hyperchaotic generalized n-D Hénon-like maps.

scholarly journals Thermal electron anisotropy driven by kinetic Alfven waves in the Earth's magnetotail

2020 ◽  
Author(s):  
Alexander Lukin ◽  
Anton Artemyev ◽  
Evgeny Panov ◽  
Rumi Nakamura ◽  
Anatoly Petrukovich ◽  
...  
Keyword(s):  
Electric Fields ◽  
Electromagnetic Waves ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Plasma Flows ◽  
Thermal Electron ◽  
Electron Population ◽  
Electron Field ◽  
Kinetic Alfvén Waves

Abstract. Thermal and subthermal electron populations in the Earth's magnetotail are usually characterized by pronounced field-aligned anisotropy that contributes to generation of strong electric currents within the magnetotail current sheet. Formation of this anisotropy requires electron field-aligned acceleration, and thus likely involves field-aligned electric fields. Such fields can be carried by various electromagnetic waves generated by fast plasma flows interacting with ambient magnetotail plasma. In this paper we consider one of the most intense observed wave emissions, kinetic Alfven waves, that often accompany fast plasma flows in the magnetotail. Using two tail seasons (2017, 2018) of MMS observations we have collected statistics of 80 fast plasma flows (or bursty bulk flows) events with distinctive enhancement of intensity of broadband electromagnetic waves (kinetic Alfven waves). We show correlation the intensity of electric fields of kinetic Alfven waves and characteristics of electron anisotropy distributions: the parallel electron anisotropy increases with magnitude of the wave parallel electric field. Also the energy range of this electron anisotropic population is well within the expected acceleration range for assumed kinetic Alfven waves. Our results indicate an important role of KAWs in production of thermal field-aligned electron population typically observed in the Earth's magnetotail.

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