Limits to chaotic phase synchronization

Zhao, Liang; Lai, Ying–Cheng; Wang, R.; Gao, Jigang

doi:10.1209/epl/i2003-10220-2

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…Specifically, the parameters of each Rössler oscillator are set as the same values used in (Rosenblum et al, 1996). Thus, each Rössler oscillator presents a phase-coherent chaotic attractor (Zhao et al, 2004(Zhao et al, , 2005. The coupling structure is similar to the model presented in (Osipov et al, 1997), i.e., each oscillator in the network is coupled to some of its eight nearest neighbors with similar color values.…”

Section: Model Descriptionmentioning

confidence: 99%

Chaotic phase synchronization and desynchronization in an oscillator network for object selection

et al. 2009

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Object selection refers to the mechanism of extracting objects of interest while ignoring other objects and background in a given visual scene. It is a fundamental issue for many computer vision and image analysis techniques and it is still a challenging task to artificial visual systems. Chaotic phase synchronization takes place in cases involving almost identical dynamical systems and it means that the phase difference between the systems is kept bounded over the time, while their amplitudes remain chaotic and may be uncorrelated. Instead of complete synchronization, phase synchronization is believed to be a mechanism for neural integration in brain. In this paper, an object selection model is proposed. Oscillators in the network representing the salient object in a given scene are phase synchronized, while no phase synchronization occurs for background objects. In this way, the salient object can be extracted. In this model, a shift mechanism is also introduced to change attention from one object to another. Computer simulations show that the model produces some results similar to those observed in natural vision systems.

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Section: Model Descriptionmentioning

confidence: 99%

Chaotic phase synchronization and desynchronization in an oscillator network for object selection

et al. 2009

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“…In the symmetrically coupled non-identical Lorenz systems, it is found that the PS point is very close to the GS point [24]. For confirming it, let us calculate the largest transverse Lyapunov exponent λ T from the model equations.…”

mentioning

confidence: 75%

Detection of phase locking from non-stationary time series

Liu

Iasemidis

2005

Europhys. Lett.

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The detection of the interrelation between non-stationary time series is a key problem unsolved in the analysis of practical data. Here we present a novel approach to detect the phase locking of time series in non-stationary status, which does not need the reconstruction of the attractor but gets information from the consistence of local rotation speeds. This method can be conveniently used for practical situations, such as the epileptic seizure.

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“…Examples include Josephson junction arrays [2], semiconductor lasers arrays [3], flashing fireflies [4], cardiac pacemaker cells [5], Parkinson's disease [6], and many others [7,8]. It is also a fundamental dynamical behavior attracting great theoretical interest [9][10][11][12][13][14][15][16][17][18][19][20]. The most tractable model to describe synchronization is the Kuramoto model [21][22][23][24], which ignores amplitude information and considers phase information of oscillators only.…”

mentioning

confidence: 99%

Synchronizing large number of nonidentical oscillators with small coupling

Wu¹,

Xiao²,

Hu³

et al. 2012

EPL

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The topic of synchronization of oscillators has attracted great and persistent interest, and all previous conclusions and intuitions have convinced that large coupling is required for synchronizing a large number of coupled nonidentical oscillators. Here the influences of different spatial frequency distributions on the efficiency of frequency synchronization are investigated by studying arrays of coupled oscillators with diverse natural frequency distributions. A universal log-normal distribution of critical coupling strength Kc for synchronization irrespective of the initial natural frequency is found. In particular, a physical quantity "roughness" R of spatial frequency configuration is defined, and it is found that the efficiency of synchronization increases monotonously with R. For large R we can reach full synchronization of arrays with a large number of oscillators at finite Kc. Two typical kinds of synchronization, the "multiple-clustering" one and the "single-center-clustering" one, are identified for small and large R's, respectively. The mechanism of the latter type is the key reason for synchronizing long arrays with finite Kc.

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Limits to chaotic phase synchronization

Cited by 9 publications

References 24 publications

Chaotic phase synchronization and desynchronization in an oscillator network for object selection

Chaotic phase synchronization and desynchronization in an oscillator network for object selection

Detection of phase locking from non-stationary time series

Synchronizing large number of nonidentical oscillators with small coupling

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