Forcing oscillatory media: phase kinks vs. synchronization

Chaté, Hugues; Pikovsky, Arkady; Rudzick, Oliver

doi:10.1016/s0167-2789(98)00215-2

Cited by 81 publications

(66 citation statements)

References 24 publications

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“…The natural continuation of these pioneering works was to investigate synchronization phenomena in spatially extended or infinite-dimensional systems [404][405][406][407][408][409], to test synchronization in experiments or natural systems [410][411][412][413][414][415][416][417][418][419][420][421], to study the mechanisms leading to de-synchronization [422,423], and to define unifying formal approaches that could encompass within the same framework the different synchronization phenomena [424]. A full account of the different synchronization states studied so far for chaotic systems and space-extended fields can be found in Ref.…”

Section: Introduction To Synchronizationmentioning

confidence: 99%

Complex networks: Structure and dynamics

et al. 2006

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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks' dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

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Section: Introduction To Synchronizationmentioning

confidence: 99%

Complex networks: Structure and dynamics

et al. 2006

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“…The case q = 0 has been addressed already in the literature in the context of oscillatory media [15,16]. Because of spatial reflection symmetry for q = 0 the two pulses of clockwise and counterclockwise chirality are equivalent.…”

Section: Case N = 1 Pulsesmentioning

confidence: 99%

“…Some of the contributions in the study of pattern formation induced by temporal forcing are Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17]. We are not addressing cases in which the forcing is itself the origin of the pattern-forming instability, such as for instance in Faraday waves [1,18].…”

Section: Introductionmentioning

confidence: 99%

Theory of pattern forming systems under traveling-wave forcing

et al. 2007

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The response of pattern forming systems to external forcing either spatial or temporal has received much attention for several decades. Combined spatio-temporal forcing has only been introduced recently, in particular in the form of a spatially resonant traveling-wave forcing [S. Rüdiger, D.G. Míguez, A.P. Muñuzuri, F. Sagués, J. Casademunt, Phys. Rev. Lett. 90 (2003) 128301]. Since then, both a series of experiments, in the context of Turing patterns in reaction-diffusion systems, and the development of the corresponding generic theory, have unveiled a wealth of new and unexpected phenomena. In this article we review these phenomena, we provide a unified and comprehensive description of them, and extend the theoretical analysis to new situations. We formulate the generic amplitude equations for different orders of spatial resonance for 1d and 2d patterns (stripes and hexagons). We identify and describe in detail the autonomous dynamical system which underlies the phenomenon of traveling-stripe resonance. For 1d we focus on localized solutions (kinks and pulses), their dynamics and their interaction for both 1:1 and 2:1 resonance. Specifically, we discuss the effect of wave-number mismatch (inexact resonance) combined with the non-gradient dynamics induced by the motion of the forcing, resulting in non-trivial interactions and complex spatio-temporal dynamics. Analytical results in the phase approximation are obtained, while numerical techniques are used to study the complete problem. We show that defect interaction is oscillatory with distance, allowing for the existence of locked chaotic wave trains. In 2d we discuss the modulational instabilities of striped patterns and focus mostly on the emergence of hexagons induced by traveling stripe forcing, for exact 1:1 resonance. In this case, we examine in detail the complex bifurcation scenario beyond primary instabilities. We finally discuss the problem of traveling-wave forcing in the context of a specific system, the photosensitive CDIMA reaction, where most experiments have been carried out. We compare experiments and theoretical predictions and propose other experimental systems where the study could be extended. Finally, we review related work by other authors and discuss possible further developments and open questions which hold the promise of new interesting findings.

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“…Kinks and traveling Bloch walls are elementary wave patterns under forcing conditions. Instabilities of kinks lead to backfiring and development of intermittent regimes with reproduction of amplitude defects [15,16,17]. Transverse instabilities of nonequilibrium planar Bloch walls give origin to the Bloch turbulence [6].…”

Section: The Forced Complex Ginzburg-landau Equationmentioning

confidence: 99%

“…2 (a)). Inside this region, kinks (n = 1) and Bloch walls (n = 2) traveling at a constant velocity are possible (see [12,15,16]). Moreover, wave trains formed by periodic sequences of such phase fronts can also be observed there.…”

Section: The Forced Complex Ginzburg-landau Equationmentioning

confidence: 99%

Trapping of phase fronts and twisted spirals in periodically forced oscillatory media

Rudzick

Mikhailov

2007

World Scientific Lecture Notes in Complex Systems

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The control of pattern formation is an important problem in engineering of spatially extended self-organized systems. A wide class of systems showing spontaneously formed waves and patterns can be summarized under the generic term "oscillatory media". They may be considered as a composition of a large number of coupled subsystems. The dynamics of each subsystem is oscillatory. Complex phenomena like the formation of patterns and waves or spatio-temporal chaos comes through the interaction between the subsystems. Despite such complex collective behavior the dynamics is very sensitive to feedback or to periodic forcing with frequencies close to an integer ratio of the oscillation frequency of the subsystems.A well-known example is the Belouzov-Zhabotinsky-Reaction, involving the oxidation of an organic compound by bromate in acidic solution. It is a robust oscillatory reaction with striking color changes. Spatiotemporal wave behavior is exhibited in unstirred reaction mixtures [1,2]. For this reaction, application of global periodic forcing was shown to produce various cluster patterns [3,4,5] and induce turbulent regimes [6].Another example which has been extensively studied is the catalytic CO oxidation on Pt(110). The interplay between desorption and surface diffusion of CO, reaction between the two adsorbed species, and an adsobate-driven structural change of the platinum surface can lead to oscillations of the CO and oxygen coverage [7]. In experiments where bulk oscillations were unstable and spatiotemporal chaos spontaneously developed, application of periodic forcing allowed to suppress chemical turbulence, produce intermittent regimes with cascades of amplitude defects, and generate oscillating cellular and labyrinthine patterns [8,9]. Recently, front explosions have been predicted under periodic forcing [10].

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Forcing oscillatory media: phase kinks vs. synchronization

Cited by 81 publications

References 24 publications

Complex networks: Structure and dynamics

Complex networks: Structure and dynamics

Theory of pattern forming systems under traveling-wave forcing

Trapping of phase fronts and twisted spirals in periodically forced oscillatory media

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