Coupling of chemical oscillators

Bar‐Eli, K.

doi:10.1021/j150660a048

Cited by 86 publications

(40 citation statements)

References 3 publications

(4 reference statements)

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“…In addition, when the cells are very different, it is possible for the coupling to annihilate the oscillatory solutions. This phenomenon is known as oscillator death, and was first reported by Bar-Eli (1984, 1985 for chemical oscillators, and Yamaguchi and Shimizu (1984) in the more general context of a large population of oscillators with a spread of natural frequencies. Oscillator death has also been studied by Aronson et al (1990) and .…”

Section: Introductionmentioning

confidence: 95%

Diffusively Coupled Bursters: Effects of Cell Heterogeneity

Vries

Sherman

Zhu

1998

Bulletin of Mathematical Biology

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The interaction of a pair of weakly coupled biological bursters is examined. Bursting refers to oscillations in which an observable slowly alternates between phases of relative quiescence and rapid oscillatory behavior. The motivation for this work is to understand the role of electrical coupling in promoting the synchronization of bursting electrical activity (BEA) observed in the β-cells of the islet of Langerhans, which secrete insulin in response to glucose. By studying the coupled fast subsystem of a model of BEA, we focus on the interaction that occurs during the rapid oscillatory phase. Coupling is weak, diffusive and non-scalar. In addition, non-identical oscillators are permitted. Using perturbation methods with the assumption that the uncoupled oscillators are near a Hopf bifurcation, a reduced system of equations is obtained. A detailed bifurcation study of this reduced system reveals a variety of patterns but suggests that asymmetrically phase-locked solutions are the most typical. Finally, the results are applied to the unreduced full bursting system and used to predict the burst pattern for a pair of cells with a given coupling strength and degree of heterogeneity.

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Section: Introductionmentioning

confidence: 95%

Diffusively Coupled Bursters: Effects of Cell Heterogeneity

Vries

Sherman

Zhu

1998

Bulletin of Mathematical Biology

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“…The PRC in Fig. 4 (1) and Df end grow almost linearly with f tending to 0 at f = 1. Regions (i) and (iii) are analogous to the experimentally obtained dependence in Fig.…”

Section: A Prcmentioning

confidence: 84%

“…5 (illustration of important dependencies). We measured Df (1) and Df end . If T = T end (after a large number of perturbations), then the period T becomes insensitive to perturbations [see Fig.…”

Section: A Prcmentioning

confidence: 99%

New type of excitatory pulse coupling of chemical oscillators via inhibitor

Proskurkin

Vanag

2015

Phys. Chem. Chem. Phys.

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We introduce a new type of pulse coupling between chemical oscillators. A constant inflow of inhibitor in one reactor is interrupted shortly after a time delay after a sharp spike of activity in the other reactor. We proved experimentally and theoretically that this reversed inhibitory coupling is analogous to excitatory coupling. We did this by analyzing phase response curves, dependences of different synchronous regimes of the 1 : 1 resonance on time delay, and other resonances of two coupled chemical oscillators. Dynamical rhythms of two Belousov-Zhabotinsky oscillators coupled via "negative" inhibitory pulses were investigated.

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“…The dynamic characteristics may involve complex network dynamic phenomena such as synchronization, hysteresis, phase lock and shift (Kaneko, 1993;Ott, 2002;Pecora and Carroll, 1990). Among the remarkable phenomena, amplitude death refers to the dynamic stability for the network structure system (Bar-Eli, 1984). Different from the traditional concept of stability, amplitude death means that the oscillation of all oscillators in the network system collectively tends to zero motion in autonomous networks (Saxena et al, 2012) or a suppressed weak oscillatory state in nonautonomous networks (Resmi et al, 2011) due to the interaction among coupled oscillators.…”

Section: Introductionmentioning

confidence: 99%

Network dynamic stability of floating airport based on amplitude death

Zhang

et al. 2015

Ocean Engineering

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Coupling of chemical oscillators

Cited by 86 publications

References 3 publications

Diffusively Coupled Bursters: Effects of Cell Heterogeneity

Diffusively Coupled Bursters: Effects of Cell Heterogeneity

New type of excitatory pulse coupling of chemical oscillators via inhibitor

Network dynamic stability of floating airport based on amplitude death

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