GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

scholarly journals ON SELF-ORGANIZED CRITICALITY AND SYNCHRONIZATION IN LATTICE MODELS OF COUPLED DYNAMICAL SYSTEMS

1996 ◽  
Vol 10 (10) ◽  
pp. 1111-1151 ◽  
Author(s):  
CONRAD J. PÉREZ ◽  
ÁLVARO CORRAL ◽  
ALBERT DÍAZ-GUILERA ◽  
KIM CHRISTENSEN ◽  
ALEX ARENAS
Keyword(s):  
Dynamical Systems ◽  
Critical Phenomena ◽  
Collective Behavior ◽  
Phase Locking ◽  
Lattice Models ◽  
Stick Slip ◽  
Integrate And Fire ◽  
Self Organized ◽  
Self Organized Criticality ◽  
The Individual

Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more complicated attractors. In some cases, these states are identified with self-organized critical phenomena. In other situations, they are identified with clusterization or phase-locking. The conditions leading to such different behaviors in models of integrate-and-fire oscillators and stick-slip processes are reviewed.

scholarly journals Using noise to augment synchronization among oscillators

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jaykumar Vaidya ◽  
Mohammad Khairul Bashar ◽  
Nikhil Shukla
Keyword(s):  
White Noise ◽  
Coupling Strength ◽  
Coupled System ◽  
External Noise ◽  
Capacitive Coupling ◽  
Frequency Locking ◽  
Relaxation Oscillators ◽  
Computing Platforms ◽  
Analog Systems ◽  
Computational Properties

AbstractNoise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms.

scholarly journals Emergence of Planck’s Constant from Iterated Maps

2020 ◽  
Author(s):  
Ervin Goldfain
Keyword(s):  
Dynamical Systems ◽  
Complex Dynamics ◽  
Phase Locking ◽  
Scaling Behavior ◽  
Asymptotic Limit ◽  
Circle Maps ◽  
Planck’S Constant ◽  
Iterated Maps ◽  
Continuous Maps ◽  
Route To Chaos

Iterations of continuous maps are the simplest models of generic dynamical systems. In particular, circle maps display several key properties of complex dynamics, such as phase-locking and the quasi-periodicity route to chaos. Our work points out that Planck’s constant may be derived from the scaling behavior of circle maps in the asymptotic limit.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

FREQUENCY SYNCHRONIZATION IN NETWORKS OF COUPLED OSCILLATORS, A MONOTONE DYNAMICAL SYSTEMS APPROACH

2009 ◽  
Vol 19 (12) ◽  
pp. 4107-4116 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Systems Approach ◽  
System Size ◽  
Coupling Scheme ◽  
Frequency Synchronization ◽  
Nonlinear Coupling ◽  
New Approach ◽  
Monotone Dynamical Systems

We propose a new approach to investigate the frequency synchronization in networks of coupled oscillators. By making use of the theory of monotone dynamical systems, we show that frequency synchronization occurs in networks of coupled oscillators, provided the coupling scheme is symmetric, connected, and strongly cooperative. Our criterion is independent of the system size, the coupling strength and the details of the connections, and applies also to nonlinear coupling schemes.

scholarly journals EEGIFT: Group Independent Component Analysis for Event-Related EEG Data

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Tom Eichele ◽  
Srinivas Rachakonda ◽  
Brage Brakedal ◽  
Rune Eikeland ◽  
Vince D. Calhoun
Keyword(s):  
Independent Component Analysis ◽  
Phase Locking ◽  
Group Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Group Model ◽  
Simulated Event ◽  
Latency Jitter ◽  
The Individual ◽  
Order Components

Independent component analysis (ICA) is a powerful method for source separation and has been used for decomposition of EEG, MRI, and concurrent EEG-fMRI data. ICA is not naturally suited to draw group inferences since it is a non-trivial problem to identify and order components across individuals. One solution to this problem is to create aggregate data containing observations from all subjects, estimate a single set of components and then back-reconstruct this in the individual data. Here, we describe such a group-level temporal ICA model for event related EEG. When used for EEG time series analysis, the accuracy of component detection and back-reconstruction with a group model is dependent on the degree of intra- and interindividual time and phase-locking of event related EEG processes. We illustrate this dependency in a group analysis of hybrid data consisting of three simulated event-related sources with varying degrees of latency jitter and variable topographies. Reconstruction accuracy was tested for temporal jitter 1, 2 and 3 times the FWHM of the sources for a number of algorithms. The results indicate that group ICA is adequate for decomposition of single trials with physiological jitter, and reconstructs event related sources with high accuracy.

scholarly journals Galvanic Phase Coupling of Superconducting Flux Qubits

2021 ◽  
Vol 11 (23) ◽  
pp. 11309
Author(s):  
Mun Dae Kim
Keyword(s):  
Coupling Strength ◽  
Fault Tolerant ◽  
Coupled System ◽  
Inductive Coupling ◽  
Galvanic Coupling ◽  
Flux Qubits ◽  
Superconducting Flux Qubits ◽  
Qubit Gate ◽  
Central Loop ◽  
Fundamental Boundary

We investigate the galvanic coupling schemes of superconducting flux qubits. From the fundamental boundary conditions, we obtain the effective potential of the coupled system of two or three flux qubits to provide the exact Lagrangian of the system. While usually the two-qubit gate has been investigated approximately, in this study we derive the exact inductive coupling strength between two flux qubits coupled directly and coupled through a connecting central loop. We observe that the inductive coupling strength needs to be included exactly to satisfy the criteria of fault-tolerant quantum computing.

scholarly journals Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package

2021 ◽  
Author(s):  
Nico Wunderling ◽  
Jonathan Krönke ◽  
Valentin Wohlfarth ◽  
Jan Kohler ◽  
Jobst Heitzig ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Open Source Software ◽  
Software Package ◽  
Model Systems ◽  
Stochastic Dynamical Systems ◽  
Moisture Recycling ◽  
Modelling Framework ◽  
Different Types ◽  
Open Source Software Package ◽  
The Individual

AbstractTipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent of each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network.

scholarly journals Quantum synchronization and correlations of two qutrits in a non-Markovian bath

2020 ◽  
Vol 18 (03) ◽  
pp. 2050005 ◽  
Author(s):  
Jian-Song Zhang
Keyword(s):  
Coupling Strength ◽  
Correlation Time ◽  
Phase Locking ◽  
Direct Interaction ◽  
Equation Method ◽  
Markovian Environment ◽  
Arnold Tongue ◽  
Quantum Synchronization ◽  
Rotating Wave ◽  
The Common

We investigate quantum synchronization and correlations of two qutrits in one non-Markovian environment using the hierarchy equation method. There is no direct interaction between two qutrits and each qutrit interacts with the same non-Markovian environment. The influence of the temperature of the bath, correlation time and coupling strength between qutrits and bath on the quantum synchronization and correlations of two qutrits are studied without the Markovian, Born and rotating wave approximations. We also discuss the influence of dissipation and dephasing on the synchronization of two qutrits. In the presence of dissipation, the phase locking between two qutrits without any direct interaction can be achieved when each qutrit interacts with the common bath. Two qutrits within one common bath cannot be syncrhonized in the purely dephasing case. In addition, the Arnold tongue can be significantly broadened by decreasing the correlation time of two qutrits and bath. Markovian baths are more suitable for synchronizing qutrits than non-Markovian baths.

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