Renormalization of oscillator lattices with disorder

Östborn, Per

doi:10.1103/physreve.79.051114

Cited by 8 publications

(10 citation statements)

References 49 publications

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“…. Substituting this ansatz into (14) leads to a evolution equation for each mode f m (r, t). We then set f m (r, t) = e λmt c m (r) and derive the following eigenvalue equation:…”

Section: Resultsmentioning

confidence: 99%

“…Kuramoto's model in turn has been generalized to other large systems of biological oscillators, such as chorusing frogs [6], firing neurons [7][8][9][10][11], and even human concert audiences clapping in unison [12]. The analyses often borrow techniques from statistical physics, such as mean-field approximations, renormalization group analyses [13,14], and finite-size scaling [15,16]. There has also been traffic in the other direction, from biology back to physics.…”

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confidence: 99%

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Oscillators that sync and swarm

2017

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Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact.

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“…. Substituting this ansatz into (14) leads to a evolution equation for each mode f m (r, t). We then set f m (r, t) = e λmt c m (r) and derive the following eigenvalue equation:…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Oscillators that sync and swarm

2017

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“…Spatial networks of spiking elements can exhibit a variety of dynamical behaviors [23][24][25][26][27]. We here reported on a novel phenomenon, namely recurrent events of synchrony, emerging robustly from networks of identical, deterministic oscillators.…”

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confidence: 96%

Recurrent events of synchrony in complex networks of pulse-coupled oscillators

Rothkegel

Lehnertz

2011

EPL

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-We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may be separated by periods of asynchrony with varying duration. The phenomenon is specific to spatial networks with both short-and longranged connections and requires delayed interactions and refractoriness of oscillators.Nature possesses various examples of systems composed of many oscillatory elements in which, through mutual interactions, collective dynamics emerges [1][2][3]. In many biological networks (like the heart or the brain) interactions are short-lasting and may be modeled as pulses, which are fired at a given oscillator phase [4,5]. Such pulse-coupled oscillators show, for large arrangements, a variety of collective dynamics with a convergence of global observables after transients. Examples range from stable synchronous [5,6] and asynchronous states [7], phase-locking [8], partial synchrony [9][10][11], to transitions from asynchronous to synchronous states [12]. The human brain with its 100 billion neurons, however, may show recurrent changes in global synchrony (as seen, e.g., on the electroencephalogram) associated with physiologic or pathophysiologic functioning [13,14].In this Letter, we present a spatial network model of pulse-coupled oscillators (PCOs), which shows collective dynamics with no convergence to either synchrony, partial synchrony, or asynchrony. Instead, the network generates -even without noise influences or a change of parameters -recurrent events that are comprised of an increase and decline in synchrony. Events may occur at random looking times and be separated by prolonged periods of asynchrony. Events may also be initiated immediately after completion of the preceding event leading to an oscillatory behavior. The oscillators thus generate a rhythm, which is not directly linked to their intrinsic time-scales (the delay of interactions and the duration of the refractory period) but is an emerging property of the network.We study networks of oscillators n ∈ N with phases φ n (t) ∈ [0, 1], dφn dt = 1. If for some t f and some oscillator n the phase reaches 1 (φ n (t f ) = 1), it is reset to 0 (φ n (t + f ) = 0) and we introduce a phase jump in all oscillators n which are adjacent to n according to some directed graph:∆ denotes the phase response curve. A refractory period of length ϑ can easily be incorporated into ∆ by setting ∆(φ) = 0 for φ < ϑ. Consider identical time delays τ < ϑ on all outgoing connections of oscillator n, such that all its excitations are received when φ n = τ . In this case, n can be replaced equivalently with an undelayed oscillator with periodically shifted phase and phase response curve. We can thus incorporate both refractoriness and delay into an arbitrary phase response curve ∆ (yielding an formally undelayed phase response curve ∆) by setting:Here denotes some coupling strength. Our choice for ∆ (φ) is...

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“…additionally, scholars ranged between interpretations that saw Baalism as displacing Yahwism, and those that hypothesized an amalgamation and identification of Yahweh with Baal. No agreement emerged, however, over the precise identity of the singular, canaanite 'Baal' in question, with proposals including Baal-shamem, Baal-Hadad, and others (see Eissfeldt 1939;Östborn 1956;Wolff 1974;andersen and Freedman 1980). Even so, in the mind of most interpreters, the majority or entirety of the various religious elements and practices mentioned in Hosea were condemned because they had become co-opted or at least tainted by the worship of Baal.…”

Section: Tradition and Redactionmentioning

confidence: 99%

“…the first category of metaphor study, which explores the book's images for God and the people, is the most common, with some emerging engagement with Hosea's depictions of the natural world and their ecological implications (e.g., loya 2008). commentaries from throughout the twentieth century highlight the use of family images (husband-wife, parentchild) as the major depictions of the relationship between God and the people, but also stress the vast array of metaphors used for both God and the people, especially in the oracles in Hosea 4-14 (see Östborn 1956;Wolff 1974;limburg 1988). these metaphors fall into several clusters, including representations of God with personal imagery (judge, farmer, physician), animal imagery (moth, lion, she-bear), and plant imagery (cypress tree, rottenness), as well as representations of the people with similar animal and agricultural metaphors (stubborn heifer, silly dove, grapes, cake, chaff).…”

Section: New Lines Of Inquirymentioning

confidence: 99%

Hosea 4—14 in Twentieth-Century Scholarship

Kelle

2010

Currents in Biblical Research

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Twentieth-century scholarship on Hosea has addressed a wide range of interpretive questions that often reflect the common approaches to the prophetic literature in general, yet an inordinate amount of attention has been paid to the marriage and family imagery in Hosea 1—3. In recent years, scholars have corrected this tendency, exploring ways that texts throughout Hosea 4—14 offer insights into long-standing critical issues. Rather than exhibiting a movement in which newer methodological perspectives have replaced older traditional approaches, all of the established, modern scholarly pursuits remain prominent in the current study of Hosea 4—14. Scholars are now reformulating the traditional questions, however, from new angles largely generated by interdisciplinary influences. These influences have also given rise to previously unexplored lines of inquiry, such as synchronic, literary, and theological readings, Book of the Twelve studies, and metaphor theory. Studies using metaphor theory with an eye toward religious, political, socio-economic, and gender considerations seem likely to occupy the central place in Hosea scholarship in the immediate future.

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Renormalization of oscillator lattices with disorder

Cited by 8 publications

References 49 publications

Oscillators that sync and swarm

Oscillators that sync and swarm

Recurrent events of synchrony in complex networks of pulse-coupled oscillators

Hosea 4—14 in Twentieth-Century Scholarship

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