The synchronization of chaotic systems

Boccaletti, Stefano; Kurths, Jürgen; Osipov, Grigory V.; Valladares, D.L.; Zhou, Changsong

doi:10.1016/s0370-1573(02)00137-0

Cited by 2,468 publications

(1,615 citation statements)

References 316 publications

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“…In our experiment, we saw periods of coherencies and without coherencies supporting this theoretical finding. Phase slips (or phase drifts; Supplementary Figs S4 and S5) can also occur close to the boarder of the phase synchronization region and are a transition stage to synchronization of chaotic dynamics 49 . However, we cannot discriminate between patterns such as on-off intermittency as a result of unequal coupling, jumps in phase differences because the system is close to a phase synchronization region or a lack of more accurate analytical tools for short time series 32 .…”

Section: Discussionmentioning

confidence: 99%

Different types of synchrony in chaotic and cyclic communities

Becks

Arndt

2013

Nat Commun

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Stability and persistence of populations is of great interest for management and conservation purposes. Spatial dynamics can have a crucial role in population stability via synchronization, and beneficial and detrimental effects on population persistence have been shown. Despite a theoretical understanding of synchronization, empirical data on synchrony of populations are restricted to systems that do not display the full spectrum of complex dynamics that may occur in nature (that is, chaos or quasiperiodicity). Here we show in experiments that the qualitative form of dynamic behaviour of chaotic and periodic oscillating communities did not change when unidirectionally coupled to oscillating driver communities. Driver and response populations were phase locked in cyclic communities, whereas chaotic communities showed only short periods of statistical coherencies. Our study provides the first empirical analysis of synchronization of chaotic communities and shows that the likelihood for chaos is not lowered in spatially explicit systems but that cyclic and chaotic systems differ in synchronization.

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Section: Discussionmentioning

confidence: 99%

Different types of synchrony in chaotic and cyclic communities

Becks

Arndt

2013

Nat Commun

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“…Two pendula, mounted together, will always end up swinging in exactly opposite directions, regardless of their respective individual motion. This was one of the first observations of the phenomenon of the coupled harmonic oscillators, which have many applications in physics [89,16,[18][19][20]47,93,5,99], biology and chemistry [93,60,63,64,100,104]. In engineering very spectacular was synchronization of pedestrians on Millennium bridge [1,19,36,37,42,81,84,86].…”

Section: Introductionmentioning

confidence: 94%

Synchronization of clocks

et al. 2012

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Abstract:In this report we recall the famous Huygens' experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging on the same beam can show the almost complete (in-phase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century. We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendula via oscillating beam allowing the pendula's synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given.

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“…There is considerable interest in networks in diverse areas of the sciences, spurred by the realization that these ideas have wide applicability [107]. The internet, food webs, neural networks, electrical power grids, coauthorship and citation networks of scholars, biological networks are well known instances [107,108,109].…”

Section: Amplitude Death On Networkmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

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The synchronization of chaotic systems

Cited by 2,468 publications

References 316 publications

Different types of synchrony in chaotic and cyclic communities

Different types of synchrony in chaotic and cyclic communities

Synchronization of clocks

Amplitude death: The emergence of stationarity in coupled nonlinear systems

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