Phase transitions towards frequency entrainment in large oscillator lattices

Östborn, Per; Åberg, Sven; Öhlén, Gunnar

doi:10.1103/physreve.68.015104

Cited by 9 publications

(13 citation statements)

References 15 publications

(16 reference statements)

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“…The node is populated by millions of cells, each a small oscillator with a natural frequency of its own (Ostborn et al, 2003). In the healthy heart these frequencies are phase locked, enabling the node to produce regular contraction commands.…”

Section: Introductionmentioning

confidence: 99%

Music structure determines heart rate variability of singers

Vickhoff¹,

Malmgren²,

Åström³

et al. 2013

Front. Psychol.

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Choir singing is known to promote wellbeing. One reason for this may be that singing demands a slower than normal respiration, which may in turn affect heart activity. Coupling of heart rate variability (HRV) to respiration is called Respiratory sinus arrhythmia (RSA). This coupling has a subjective as well as a biologically soothing effect, and it is beneficial for cardiovascular function. RSA is seen to be more marked during slow-paced breathing and at lower respiration rates (0.1 Hz and below). In this study, we investigate how singing, which is a form of guided breathing, affects HRV and RSA. The study comprises a group of healthy 18 year olds of mixed gender. The subjects are asked to; (1) hum a single tone and breathe whenever they need to; (2) sing a hymn with free, unguided breathing; and (3) sing a slow mantra and breathe solely between phrases. Heart rate (HR) is measured continuously during the study. The study design makes it possible to compare above three levels of song structure. In a separate case study, we examine five individuals performing singing tasks (1–3). We collect data with more advanced equipment, simultaneously recording HR, respiration, skin conductance and finger temperature. We show how song structure, respiration and HR are connected. Unison singing of regular song structures makes the hearts of the singers accelerate and decelerate simultaneously. Implications concerning the effect on wellbeing and health are discussed as well as the question how this inner entrainment may affect perception and behavior.

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Section: Introductionmentioning

confidence: 99%

Music structure determines heart rate variability of singers

Vickhoff¹,

Malmgren²,

Åström³

et al. 2013

Front. Psychol.

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“…When d ജ 2, states with 0 Ͻ r Ͻ 1 are possible and may appear when the natural frequency distribution has tails or the coupling is not strong enough to allow perfect entrainment. There is numerical evidence for such states [11], but analytical results are again lacking. ACKNOWLEDGMENT I thank Bernhard Mehlig, who suggested that I do the present work.…”

Section: Discussionmentioning

confidence: 95%

“…(4)]. In addition, we limited ourselves to coupling functions ⌫͑x͒ fulfilling either case (10) or (11). The last limitation is not essential if we just want to make sure that there is a critical coupling.…”

Section: Discussionmentioning

confidence: 99%

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Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit

Östborn

2004

Phys. Rev. E

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We study oscillator chains of the form phi; (k) = omega(k) +K[Gamma( phi(k-1) - phi(k) )+Gamma( phi(k+1) - phi(k) )], where phi(k) epsilon[0,2pi) is the phase of oscillator k. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of Gamma(x), we prove that there is a critical coupling strength K(c), above which a stable frequency-entrained state exists, but below which the probability is zero to have such a state. It is assumed that the natural frequencies are random with finite bandwidth. A crucial condition on Gamma(x) is that it is nonodd, i.e., mid R: Gamma(x)+Gamma(-x) mid R: not equal 0. The interest in the results comes from the fact that any chain of limit-cycle oscillators can be described by equations of the above form in the limits of weak coupling and narrow distribution of natural frequencies.

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“…Several theoretical studies on diffusive coupling have appeared in the literature in recent years. Some of them concentrate on mathematical theory (5)(6)(7)(8) and others include physiological aspects (9)(10)(11). Although diffusive coupling is more common and realistic in many physical systems (12)(13)(14), it is neither well understood nor widely studied compared to the global coupling (12,13,15).…”

Section: Introductionmentioning

confidence: 99%

Diffusive Coupling and Network Periodicity: A Computational Study

Park

Feng

Durand

2008

Biophysical Journal

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Diffusive coupling (nearest-neighbor coupling) is the most common type of coupling present in many systems. Previous experimental and theoretical studies have shown that potassium lateral diffusion coupling (i.e., diffusive coupling) can be responsible for synchronization of neuronal activity. Recent in vivo experiments carried out with anesthetized rat hippocampus suggested that the extracellular potassium could play an important role in the generation of a novel type of epileptiform nonsynaptic activity. Yet, the role of potassium in the generation of seizures remains controversial. We tested the hypothesis that potassium lateral diffusion coupling is responsible for the coupling mechanisms for network periodicity in a nonsynaptic model of epilepsy in vivo using a CA1 pyramidal neuron network model The simulation results show that 1), potassium lateral diffusion coupling is crucial for establishing epileptiform activity similar to that generated experimentally; and 2), there exists a scaling relation between the critical coupling strength and the number of cells in the network. The results not only agree with the theoretical prediction, but strongly suggest that potassium lateral diffusion coupling, a physiological realization of the concept of diffusive coupling, can play an important role in entraining periodicity in a nonsynaptic neural network.

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Phase transitions towards frequency entrainment in large oscillator lattices

Cited by 9 publications

References 15 publications

Music structure determines heart rate variability of singers

Music structure determines heart rate variability of singers

Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit

Diffusive Coupling and Network Periodicity: A Computational Study

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