Cooperative phenomena observed in a globally coupled phase-locked loop system

Shirahama, Hiroyuki; Fukushima, Kazuhiro; Kojio, K.; Yamada, Tomoji

doi:10.1109/81.873884

Cited by 5 publications

(11 citation statements)

References 8 publications

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“…In the partially ordered phase, the state itinerates among various attractors, and such a transition phenomenon is called chaotic itinerancy. This phenomenon is also observed in real systems [3][4][5]. In a star-coupled map (SCM), a locally coupled system with a few degrees of freedom, such as that used as a model in the present paper, a phenomenon similar to that in GCM is observed [6].…”

supporting

confidence: 67%

“…Figure 2 shows the Lyapunov spectrum λ calculated in the partially synchronized state. As is seen in this figure, values of λ (2) , λ (3) and λ (4) are nearly equal to zero. Next, we examine the temporal behavior of these Lyapunov exponents (λ (2) , λ (3) and λ (4) ).…”

supporting

confidence: 53%

“…As is seen in this figure, values of λ (2) , λ (3) and λ (4) are nearly equal to zero. Next, we examine the temporal behavior of these Lyapunov exponents (λ (2) , λ (3) and λ (4) ). Figures 3(a)-(c) express the time-variation of locally time-averaged λ (2) , λ (3) and λ (4) in the partially synchronized state for the case of a = 3.7 and D = 0.299.…”

supporting

confidence: 53%

“…Next, we examine the temporal behavior of these Lyapunov exponents (λ (2) , λ (3) and λ (4) ). Figures 3(a)-(c) express the time-variation of locally time-averaged λ (2) , λ (3) and λ (4) in the partially synchronized state for the case of a = 3.7 and D = 0.299. In these figures, the averaging time step is set to be 512.…”

mentioning

confidence: 99%

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Lyapunov spectrum analysis for a chaotic transition phenomenon

et al. 2003

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A chaotic transition phenomenon in a five-star-coupled map system resulting from recombination of synchronized clusters is analyzed numerically with the Lyapunov spectrum. When a chaotic transition phenomenon occurs, in the Lyapunov spectrum, three Lyapunov exponents take the value of nearly zero. When we introduce a locally time-averaged Lyapunov exponent, these three Lyapunov exponents fluctuate around zero. The time-variation of the difference between two of the three local Lyapunov exponents shows an intermittent behavior very similar to on-off intermittency. In the intermittent time-variation, however, the distribution function of the laminar duration time is shown as a power law with a value of power nearly equal to −2. This power law is distinguishable from that of on-off intermittency, in which the distribution function of the laminar duration time is expressed as a − 3 2 power law. Furthermore, these results are also obtained in globally coupled systems of various system sizes. We examine the results for systems with sizes of 4, 5, 8, 16, 32 and 64.

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supporting

confidence: 67%

supporting

confidence: 53%

supporting

confidence: 53%

mentioning

confidence: 99%

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Lyapunov spectrum analysis for a chaotic transition phenomenon

et al. 2003

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“…Networks with 3 nodes have been used for representing some actual neural systems (e.g., [13]- [15]). We start analyzing this very simple network to obtain some insights that may be applied in more complex networks (e.g., [16]). Despite its simplicity, it is not easy to determine analytically the range of frequencies that would lead to global synchronism.…”

Section: Global and Partial Synchronismmentioning

confidence: 99%

Global and partial synchronism in phase-locked loop networks

Monteiro

Canto

Chauí‐Berlinck

et al. 2003

IEEE Trans. Neural Netw.

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A current‐mode 1kHz/10kHz low‐voltage integrated analogue PLL for lock‐in portable applications

Ferri

Massa

2003

Circuit Theory & Apps

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SUMMARYWe present a low-supply voltage (2 V) low-power consumption (500 W) analogue phase-locked loop (PLL), working at two low frequencies (1 and 10 kHz), to be used in an integrated lock-in ampliÿer. An externally settable control bit allows the switching operation between the two di erent frequencies. The circuit has been designed in a standard 0.6 -m CMOS technology and di ers from the standard analogue PLL architectures for the current mode implementation of both the loop ÿlter and of the oscillator. Three di erent locked waveforms (sinusoidal, triangular, squared) can be obtained at the PLL output. Simulation results, obtained through the use of PSPICE and using accurate transistor models, will be proposed. The pull-in ranges are about ±250 Hz around 1 and ±1:3 kHz around 10 kHz, with pull-in times of about 10 and 4 ms, respectively.

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Cooperative phenomena observed in a globally coupled phase-locked loop system

Cited by 5 publications

References 8 publications

Lyapunov spectrum analysis for a chaotic transition phenomenon

Lyapunov spectrum analysis for a chaotic transition phenomenon

Global and partial synchronism in phase-locked loop networks

A current‐mode 1kHz/10kHz low‐voltage integrated analogue PLL for lock‐in portable applications

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