DISORDER INDUCED ORDER IN AN ARRAY OF CHAOTIC DUFFING OSCILLATORS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250071 ◽  
Author(s):  
YOUMING LEI ◽  
FULI GUAN
Keyword(s):  
Intermediate Phase ◽  
Duffing Oscillator ◽  
Random Phase ◽  
Practical Method ◽  
Spatially Extended ◽  
Potential Applications ◽  
Spatially Extended Systems ◽  
The Common ◽  
Spatio Temporal ◽  
Control And Synchronization

This paper addresses the issue of disorder induced order in an array of coupled chaotic Duffing oscillators which are excited by harmonic parametric excitations. In order to investigate the effect of phase disorder on dynamics of the array, we take into account that individual uncoupled Duffing oscillator with a parametric excitation is chaotic no matter what the initial phase of the excitation is. It is shown that phase disorder by randomly choosing the initial phases of excitations can suppress spatio-temporal chaos in the system coupled by chaotic Duffing oscillators. When all the phases are the same and deterministic, the oscillators remain chaotic and asynchronous no matter what the common phase is. When driven asynchronously by introducing phase disorder, the oscillators coupled in the array appear more regular with increase of the amplitude of random phase, and the highest level of synchrony between them is induced by intermediate phase disorder, displaying a resonance like phenomenon caused from the transition of the coupled oscillators from chaos to periodic motion. Since varying the initial phases of excitations is more feasible than altering parameters intrinsic to the oscillators coupled in an array, this study provides a practical method for control and synchronization of chaotic dynamics in high-dimensional, spatially extended systems, which might have potential applications in engineering, neuroscience and biology.

scholarly journals Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Alexander McDonald ◽  
Aashish A. Clerk
Keyword(s):  
Skin Effect ◽  
Tight Binding ◽  
Quantum Fisher Information ◽  
System Size ◽  
Distinct Advantage ◽  
Lattice Systems ◽  
Spatially Extended ◽  
Potential Applications ◽  
Spatially Extended Systems ◽  
Quantum Optical

Abstract Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a $${{\mathbb{Z}}}_{2}$$ Z 2 symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.

CHARACTERIZATION OF ASYMMETRIC FRAGMENTATION PATTERNS IN SPATIALLY EXTENDED SYSTEMS

1999 ◽  
Vol 10 (01) ◽  
pp. 147-163 ◽  
Author(s):  
R. R. ROSA ◽  
A. S. SHARMA ◽  
J. A. VALDIVIA
Keyword(s):  
Structural Complexity ◽  
Quantitative Measure ◽  
Gradient Field ◽  
Extended Systems ◽  
Fragmentation Parameter ◽  
Spatially Extended ◽  
Spatially Extended Systems ◽  
Spatio Temporal ◽  
Fragmentation Patterns

Spatially extended systems yield complex patterns arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator, [Formula: see text], for the characterization of asymmetric amplitude fragmentation in extended systems. For a given matrix of amplitudes this operation results in an asymmetric-triangulation field composed by L points and I straight lines. The parameter (I-L)/L is a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amplitudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator [Formula: see text] and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns.

scholarly journals NEW WAY TO ACHIEVE SYNCHRONIZATION IN SPATIALLY EXTENDED SYSTEMS

2001 ◽  
Vol 15 (16) ◽  
pp. 535-543
Author(s):  
BIKASH C. GUPTA ◽  
P. A. SREERAM ◽  
S. B. LEE
Keyword(s):  
Nearest Neighbor ◽  
Logistic Map ◽  
Periodic Boundary Conditions ◽  
Spatial Behavior ◽  
Coupled Map Lattices ◽  
Circle Map ◽  
Coupling System ◽  
Spatially Extended ◽  
Spatially Extended Systems ◽  
Spatio Temporal

We study the spatio-temporal behavior of simple unidirectionally coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, the sine circle map and the logistic map. It is found that even though the spatial behavior is irregular for the regularly coupled (nearest-neighbor coupling) system, the spatially synchronized (sometimes chaotically synchronized) as well as periodic solution may be obtained by the rearrangement of only three nearest-neighbor couplings.

Observation of Chaotic Attractor in Spatially Extended Systems: Coarse-Grained Dimension of Frozen Chaos

1999 ◽  
Vol 38 (Part 1, No. 6A) ◽  
pp. 3784-3792
Author(s):  
Donghak Choi ◽  
Nobuko Fuchikami ◽  
Eriko Hirokami ◽  
Shunya Ishioka ◽  
Masayoshi Naito
Keyword(s):  
Chaotic Attractor ◽  
Coarse Grained ◽  
Extended Systems ◽  
Spatially Extended ◽  
Spatially Extended Systems

The State and Democratization: The United States in Comparative Perspective

2004 ◽  
Vol 34 (2) ◽  
pp. 193-210 ◽  
Author(s):  
FRANCISCO E. GONZÁLEZ ◽  
DESMOND KING
Keyword(s):  
American Exceptionalism ◽  
The United States ◽  
The State ◽  
Comparative Perspective ◽  
Third Wave ◽  
Liberal Democracies ◽  
Historical Process ◽  
American Experience ◽  
The Common ◽  
Spatio Temporal

In this article we defend the importance of the concept of ‘stateness’ in scholarly understanding of political democratization. We argue that because processes of political democratization in different spatio-temporal settings often share important similarities they are therefore comparable. We investigate this proposition by comparing the process of American political democratization with those of other liberal democracies, old and new. We review extant accounts of the historical process of American democratization – including those addressing American exceptionalism, class structures, multiple traditions, social movements, and international pressures – before presenting an alternative comparative account based on the idea of stateness. Attention to stateness problems defined along legal, bureaucratic and ideological dimensions and derived from both the classic Weberian perspective on the state and the more recent ‘third wave’ of democratization theory help to place the long American experience of democratization in comparative perspective. This finding illuminates some of the common political challenges in the construction of liberal democracies, old and new.

scholarly journals Decomposing spatio-temporal seismicity patterns

2001 ◽  
Vol 1 (1/2) ◽  
pp. 83-92 ◽  
Author(s):  
C. Goltz
Keyword(s):  
Spatial And Temporal Variability ◽  
Seismicity Patterns ◽  
Seismicity Rate ◽  
Potential Applications ◽  
Time Series Approach ◽  
Distributed Process ◽  
Sample Application ◽  
Components Analysis ◽  
Spatio Temporal ◽  
Large Earthquakes

Abstract. Seismicity is a distributed process of great spatial and temporal variability and complexity. Efforts to characterise and describe the evolution of seismicity patterns have a long history. Today, the detection of changes in the spatial distribution of seismicity is still regarded as one of the most important approaches in monitoring and understanding seismicity. The problem of how to best describe these spatio-temporal changes remains, also in view of the detection of possible precursors for large earthquakes. In particular, it is difficult to separate the superimposed effects of different origin and to unveil the subtle (precursory) effects in the presence of stronger but irrelevant constituents. I present an approach to the latter two problems which relies on the Principal Components Analysis (PCA), a method based on eigen-structure analysis, by taking a time series approach and separating the seismicity rate patterns into a background component and components of change. I show a sample application to the Southern California area and discuss the promising results in view of their implications, potential applications and with respect to their possible precursory qualities.

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