scholarly journals Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 601
Author(s):  
Alexey V. Rusakov ◽  
Dmitry A. Tikhonov ◽  
Nailya I. Nurieva ◽  
Alexander B. Medvinsky
Keyword(s):  
Coupled Oscillators ◽  
Chaotic Dynamics ◽  
Threshold Value ◽  
Chaotic Oscillations ◽  
Chaotic Oscillators ◽  
Self Organized ◽  
Suppression Of Chaos

We show that interactions of inherently chaotic oscillators can lead to coexistence of regular oscillatory regimes and chaotic oscillations in the rings of coupled oscillators provided that the level of interaction between the oscillators exceeds a threshold value. The transformation of the initially chaotic dynamics into the regular dynamics in a number of the coupled oscillators is shown to result from suppression of chaos by separation of certain oscillation periods from the continuous spectra, which are characteristic of chaotic oscillations.

Online Monitoring Recognition Theory Based on the Time Series of Chatter

2013 ◽  
Vol 819 ◽  
pp. 160-164
Author(s):  
Yong Xiang Jiang ◽  
Bing Du ◽  
Pan Zhang ◽  
San Peng Deng ◽  
Yu Ming Qi
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Online Monitoring ◽  
Vibration Signal ◽  
Threshold Value ◽  
Coarse Grained ◽  
Attractor Dimension ◽  
Machining Chatter ◽  
Recognition Theory ◽  
On Line

On-line monitoring recognition for machining chatter is one of the key technologies in manufacturing. Based on the nonlinear chaotic control theory, the vibration signal discrete time series for on-line monitoring indicator is studed. As in chatter the chaotic dynamics process attractor dimension is reduced, the KolmogorovSinai entropy (K-S) index is extracted to reflected the regularity of workpiece chatter, then the k-S entropy is simplified by coarse - grained entropy rate (CER), which can easily evaluated as chatter online monitoring threshold value. The milling test shows that the CER have a sharp decline when chatter occurre, and can quickly and accurately forecast chatter.

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

STIMULUS-INDUCED CHAOTIC SYNCHRONIZATION OF CHUA'S OSCILLATORS

2006 ◽  
Vol 16 (10) ◽  
pp. 2843-2853
Author(s):  
V. V. KLINSHOV ◽  
V. B. KAZANTSEV ◽  
V. I. NEKORKIN
Keyword(s):  
Initial Phase ◽  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Cluster Formation ◽  
Time Moment ◽  
Chaotic Oscillation ◽  
Single Pulse ◽  
Chaotic Synchronization ◽  
Phase Reset ◽  
Chaotic Oscillators

The problem of phase synchronization of Chua's chaotic oscillators is investigated. We consider Chua's circuit when it exhibits a chaotic attractor and apply a single pulse stimulus. It is shown that under certain conditions the system displays self-referential phase reset (SPR) phenomenon. This is a case when the reset phase of the chaotic oscillation is independent on the initial phase, hence on the time moment when the stimulus has been applied. In an ensemble of chaotic oscillators simultaneously stimulated, the SPR yields mutual phase coherence or synchronization between the units. We describe basic dynamical mechanisms of the effect and show how it can be used for controllable cluster formation and for the control of chaotic dynamics.

TOPOLOGICAL ANALYSIS OF CHAOS IN EQUIVARIANT ELECTRONIC CIRCUITS

1996 ◽  
Vol 06 (12b) ◽  
pp. 2531-2555 ◽  
Author(s):  
C. LETELLIER ◽  
G. GOUESBET ◽  
N.F. RULKOV
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Electronic Circuit ◽  
Topological Analysis ◽  
Experimental System ◽  
Electronic Circuits ◽  
Chaotic Oscillations ◽  
Symmetry Properties

Chaotic oscillations in an electronic circuit are studied by recording two time series simultaneously. The chaotic dynamics is characterized by using topological analysis. A comparison with two models is also discussed. Some prescriptions are given in order to take into account the symmetry properties of the experimental system to perform the topological analysis.

scholarly journals Cascades of Multiheaded Chimera States for Coupled Phase Oscillators

2014 ◽  
Vol 24 (08) ◽  
pp. 1440014 ◽  
Author(s):  
Yuri L. Maistrenko ◽  
Anna Vasylenko ◽  
Oleksandr Sudakov ◽  
Roman Levchenko ◽  
Volodymyr L. Maistrenko
Keyword(s):  
Periodic Orbit ◽  
Coupled Oscillators ◽  
Phase Oscillators ◽  
Invariant Circle ◽  
Saddle Node Bifurcation ◽  
Chimera States ◽  
Chimera State ◽  
Self Organized ◽  
Saddle Node ◽  
Different Types

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.

scholarly journals Modelling the outer radiation belt as a complex system in a self-organised critical state

2005 ◽  
Vol 12 (6) ◽  
pp. 993-1001 ◽  
Author(s):  
N. B. Crosby ◽  
N. P. Meredith ◽  
A. J. Coates ◽  
R. H. A. Iles
Keyword(s):  
Radiation Belt ◽  
Outer Part ◽  
Power Laws ◽  
Threshold Value ◽  
Electron Radiation ◽  
Outer Electron ◽  
Outer Radiation Belt ◽  
Frequency Distributions ◽  
Self Organized ◽  
Self Organized Criticality

Abstract. The dynamic behaviour of the outer electron radiation belt makes this area of geo-space a candidate for the concept of self-organized criticality. It is shown here that frequency distributions of measured outer electron radiation belt data are well-represented by power-laws over two decades. Applying the concept of self-organized criticality to interpret the shape of the distributions suggests another approach to complement existing methods in the interpretation of how this complicated environment works. Furthermore sub-grouping the radiation belt count rate data as a function of spatial location or temporal interval (e.g. L-shell, magnetic local time, solar cycle, ...) shows systematic trends in the value of the slope of the power-laws. It is shown that the inner part of the outer radiation belt is influenced in a similar manner to the outer part, but in a less profound way. Our results suggest that the entire outer radiation belt appears to be affected as the sum of its individual parts. This type of study also gives the probability of exceeding a given threshold value over a given time; limiting the size of "an event". The average values could then be compared with models used in spacecraft design.

scholarly journals Analysis of Rattleback Chaotic Oscillations

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Michael Hanias ◽  
Stavros G. Stavrinides ◽  
Santo Banerjee
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Chaotic Dynamics ◽  
The Other ◽  
Strange Attractors ◽  
Rotational Behaviour ◽  
Chaotic Oscillations ◽  
Kinematic Behaviour ◽  
Ancient Times ◽  
Related Time Series

Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback’s chaotic dynamics are studied by applying Kane’s model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors’ invariant parameters.

scholarly journals Chaotic Exploration and Learning of Locomotion Behaviors

2012 ◽  
Vol 24 (8) ◽  
pp. 2185-2222 ◽  
Author(s):  
Yoonsik Shim ◽  
Phil Husbands
Keyword(s):  
Chaotic Dynamics ◽  
Neural System ◽  
Adaptive Synchronization ◽  
Rhythmic Pattern ◽  
Motor Patterns ◽  
Self Organized ◽  
Physical Environments ◽  
Wide Range ◽  
Locomotion Behavior ◽  
Articulated Robot

We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage.

scholarly journals Self-organized dynamics and the transition to turbulence of confined active nematics

2019 ◽  
Vol 116 (11) ◽  
pp. 4788-4797 ◽  
Author(s):  
Achini Opathalage ◽  
Michael M. Norton ◽  
Michael P. N. Juniper ◽  
Blake Langeslay ◽  
S. Ali Aghvami ◽  
...  
Keyword(s):  
Chaotic Dynamics ◽  
Topological Defects ◽  
Transition To Turbulence ◽  
Director Field ◽  
Self Organized ◽  
Nematic Director ◽  
Double Spiral ◽  
Circular Flows ◽  
Periodic Dynamics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of +1/2 defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.

Effects of Periodic and Stochastic Perturbations on Oscillations and Chaos in a Model of the Peroxidase-Oxidase Reaction

1985 ◽  
Vol 40 (12) ◽  
pp. 1283-1288 ◽  
Author(s):  
Lars F. Olsen
Keyword(s):  
Chaotic Dynamics ◽  
Experimental System ◽  
The Other ◽  
Random Perturbations ◽  
Chaotic Oscillations ◽  
Stochastic Perturbations ◽  
Small Random Perturbations ◽  
Periodic Dynamics ◽  
Oxidase Reaction ◽  
Small Periodic

The effects of periodic and random perturbations on the periodic and chaotic oscillations in a model of the peroxidase-oxidase reaction are investigated. The perturbations were chosen to be comparable in size and frequency to those measured in the experimental system. Small periodic perturbations did not affect the dynamics significantly. Small random perturbations, on the other hand, could totally obscure simple periodic dynamics whereas chaotic dynamics turned out to be relatively robust to such perturbations.

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