Controlling synchronous patterns in complex networks

Lin, Weijie; Fan, Huawei; Wang, Ying; Huang, Ying; Wang, Xingang

doi:10.1103/physreve.93.042209

Cited by 32 publications

(30 citation statements)

References 51 publications

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“…Additional evidences from large-size complex network possessing permutation symmetries have been also provided [43][44][45][46][47][48]. With the help of computational group theory algorithm [50], the permutation symmetries of large-size complex networks now can be identified numerically, which, combining with the generalized method of eigenvalue analysis [44,46,49,51,52], can be used to analyze the formation of cluster synchronization in the general complex networks.…”

Section: Introductionmentioning

confidence: 99%

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Chen

Wang

et al. 2018

Front. Phys.

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By a small-size complex network of coupled chaotic Hindmarsh-Rose circuits, we study experimentally the stability of network synchronization to the removal of shortcut links. It is shown that the removal of a single shortcut link may destroy either completely or partially the network synchronization. Interestingly, when the network is partially desynchronized, it is found that the oscillators can be organized into different groups, with oscillators within each group being highly synchronized but are not for oscillators from different groups, showing the intriguing phenomenon of cluster synchronization. The experimental results are analyzed by the method of eigenvalue analysis, which implies that the formation of cluster synchronization is crucially dependent on the network symmetries. Our study demonstrates the observability of cluster synchronization in realistic systems, and indicates the feasibility of controlling network synchronization by adjusting network topology. *

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Section: Introductionmentioning

confidence: 99%

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Chen

Wang

et al. 2018

Front. Phys.

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“…The form of equation (10), evidently shows that dTOS behaves same as SOS (equation (2)). On the contrary, equation (11), depicts that in case of mTOS, the perturbation η also depends upon its x-component ( x h ) in addition to coupling strength (γ) and eigenmodes (k). Moreover, since the evolution of x h does not depend on γ and k (equation (11b)), it could act as a stability factor.…”

Section: Msf In Case Of Tosmentioning

confidence: 99%

Enhancement of network synchronizability via two oscillatory system

Singh

2018

J. Phys. Commun.

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Network's synchronization destabilizes at large coupling strength when its nodes exchange information by scalar coupling (few coordinates) instead of using vector coupling (all coordinates). This issue is commonly tackled by modifying the network topology like a ring network to Small World or Scale Free networks which increases the coupling cost and decreases the robustness. In the present work, we show that without any structural alteration even a large ring network in the nearest neighborhood configuration using only a single coordinate in the coupling, could be made synchronizable. The primary condition is that the node dynamics should be given by a pair of oscillators (say, two oscillatory system TOS) rather than by a conventional way of single oscillator (say, single oscillatory system). It has been found that TOS not only stabilizes the chaotic synchronization but also the hyperchaotic synchronization manifold (a major challenge in the field of secure communication wherein multi parameter BK method is needed). The frameworks of drive-response system and master stability function have been used to study the TOS effect by varying TOS parameters with and without feedback (feedback means quorum sensing conditions). The TOS effect has been found numerically both in the chaotic (Rössler, Chua and Lorenz) and hyperchaotic (electrical circuit) systems. However, since threshold also increases as a side effect of TOS, the extent of β enhancement depends on the choice of oscillator model like larger for Rössler, intermediate for Chua and smaller for Lorenz. dsyn g ) limit the size of a synchronizable network, e.g. the synchronized state of a ring network having x 1 -coupled chaotic Rössler becomes unstable with the increase in N from 18 to 19 at dsyn g = 1.5. To tackle this issue of limited values of dsyn g , the network modification methods are generally used such as (1) adding the additional edges between the nodes deterministically (Pristine World) or/and stochastically (Small World) [5], (2) modifying the ring network topology to a synchronizable topology like a unidirectional tree network or a star network (a hub of Scale Free network) [6][7][8]. Practically these modifications could be considered as the distribution of overload among the nodes and theoretically these alterations imply the minimization of eigen-ratio (R) of the Laplacian/ coupling matrix (largest eigenvalue to the smallest nonzero eigenvalue). The concept of R minimization comes from the theory of master stability function (MSF) [9] which says that a complex network of size N is

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“…This has to be taken into account in calculating the line shapes. For higher levels, the transition rates may be better described via semi-classical description, for example using wave-packet states for the electrons [22]. In the context of new experimental facilities exploring warm dense matter [1,2,3,21], strongly coupled and nearly degenerate Coulomb systems can be produced.…”

Section: Conclusion Further Improvementsmentioning

confidence: 99%

Ionization potential depression and optical spectra in a Debye plasma model

Lin

Röpke

Reinholz

et al. 2017

Contrib. Plasma Phys

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We show how optical spectra in dense plasmas are determined by the shift of energy levels as well as by the broadening due to collisions with the plasma particles. In the lowest approximation, the interaction with the plasma particles is described by the random phase approximation (RPA) dielectric function, leading to the Debye shift of the continuum edge. The bound states remain nearly un‐shifted, and their broadening is calculated in the Born approximation. The roles of ionization potential depression as well as the Inglis–Teller effect are shown. The model calculations have to be improved going beyond the lowest (RPA) approximation when applying to warm dense matter spectra.

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Controlling synchronous patterns in complex networks

Cited by 32 publications

References 51 publications

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Enhancement of network synchronizability via two oscillatory system

Ionization potential depression and optical spectra in a Debye plasma model

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