Partial synchronization and spontaneous spatial ordering in coupled chaotic systems

Zhang, Ying; Hu, Gang; Cerdeira, Hilda A.; Chen, Shigang; Bräun, Thomas; Yao, Yugui

doi:10.1103/physreve.63.026211

Cited by 75 publications

(42 citation statements)

References 25 publications

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“…However, several previous works have pointed out that larger (less restrictive) flow-invariant subspaces may exist if the network exhibits symmetries [52,2,36], even when the systems are not identical [11].…”

Section: Symmetries and Input-equivalencementioning

confidence: 99%

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Stable concurrent synchronization in dynamic system networks

2007

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In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple "rhythms" interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flow-invariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Robustnesss of stable concurrent synchronization to variations in individual dynamics is also quantified. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed.

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Section: Symmetries and Input-equivalencementioning

confidence: 99%

“…Any of these subspaces is a strict superset of the global sync subspace, and therefore one should expect that the convergence to any of the concurrent sync state is "easier" than the convergence to the global sync state [52,2,36]. This can be quantified from (10), by noticing that…”

Section: Illustrative Examplesmentioning

confidence: 99%

Stable concurrent synchronization in dynamic system networks

2007

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“…1-3 These systems have been observed to synchronize themselves to a common frequency when the coupling strength between these oscillators is increased. [4][5][6][7][8][9][10][11][12][13] The synchronization features of many of the above-mentioned systems, in spite of the diversity of the dynamics, might be described using simple models of weakly coupled phase oscillators such as the Kuramoto model. 8,14 Finite range interactions are more realistic for the description of many physical systems, although finite range coupled systems are difficult to analyze and to solve analytically.…”

Section: Introductionmentioning

confidence: 99%

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

El‐Nashar

Muruganandam

Ferreira

et al. 2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.

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“…The higher the number of oscillators that form a network, the richer the pattern of possible synchronous states may be ͑see Ref. 15, for example͒, hence it is important to study properties of the network itself, in order to predict some of its possible synchronous states.…”

Section: Partial Synchronizationmentioning

confidence: 99%