Stability results for in-phase and splay-phase states of solid-state laser arrays

Silber, Mary; Fabiny, Larry; Wiesenfeld, Kurt

doi:10.1364/josab.10.001121

Cited by 92 publications

(48 citation statements)

References 29 publications

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“…The dynamics of coupled oscillator arrays has been the subject of much recent experimental and theoretical interest. Example systems include Josephson junctions [1,2], lasers [3], oscillatory chemical reactions [4], heart pacemaker cells [5], central pattern generators [6], and cortical neural oscillators [7]. In many applications the oscillators are identical, dissipative, and the coupling is symmetric.…”

Section: (Received 28 July 1997)mentioning

confidence: 99%

Dynamics of a Ring of Pulse-Coupled Oscillators: Group-Theoretic Approach

1997

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Section: (Received 28 July 1997)mentioning

confidence: 99%

Dynamics of a Ring of Pulse-Coupled Oscillators: Group-Theoretic Approach

1997

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“…[1][2][3][4] Its applications range from information transfer, 5 self-organized optimization of work flow or traffic flow 6 to the realization of strong coherent oscillations in arrays of Josephson junctions or coupled fiber lasers. 7 The transition to partial synchronization, i.e., the emergence of a nonzero mean field, in systems of nonidentical oscillators is well-known. It has been studied analytically in the original texts by Kuramoto 4,8 and in a more general way in recent papers.…”

Section: Introductionmentioning

confidence: 99%

Synchronization transition of identical phase oscillators in a directed small-world network

Tönjes

Masuda

Kori

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on the shortcut density and on the asymmetry of the phase coupling function, there exists a regime of persistent chaotic dynamics. By increasing the density of shortcuts or decreasing the asymmetry of the phase coupling function, we observe a discontinuous transition in the ability of the system to synchronize. Using a control technique, we identify the bifurcation scenario of the order parameter. We also discuss the relation between dynamics and topology and remark on the similarity of the synchronization transition to directed percolation. © 2010 American Institute of Physics. ͓doi:10.1063/1.3476316͔The adjustment of phase and frequency in large systems of oscillatory units can lead to global coherent oscillations, i.e., synchronization. On the other hand, noise and heterogeneity in the system can weaken synchronization, or even destroy it. Synchronization in the nervous system can facilitate the transfer of information or cause epileptic seizures. Multistability and hysteresis of normal and pathological collective behavior are observed. When all oscillators are identical and the coupling tends to decrease phase differences a state of complete synchronization is asymptotically stable. But even in random networks with uncorrelated and homogeneously distributed node degrees this absorbing state may not be reached or disappear when it is perturbed locally. Here we perform a detailed numerical analysis of the transition between different states of synchronization in a directed smallworld network of phase oscillators. By varying the mean in-degree of the network or the nonlinearity of the phase coupling function at zero phase difference, we find discontinuous and continuous transitions with mean field critical behavior.

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“…We immediately see that 7,8 can develop negative real parts for a pump amplitude greater than the critical value, ⑀ c = ␥ a ␥ b / . As it must, this expression reduces to the single OPO expression of ␥ a ␥ b / when the couplings are set to zero.…”

Section: ͑7͒mentioning

confidence: 85%

Entanglement and the Einstein-Podolsky-Rosen paradox with coupled intracavity optical down-converters

Olsen

Drummond

2005

Phys. Rev. A

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We show that two evanescently coupled ͑2͒ parametric down-converters inside a Fabry-Perot cavity provide a tunable source of quadrature squeezed light, Einstein-Podolsky-Rosen ͑EPR͒ correlations and quantum entanglement. Analyzing the operation in the below threshold regime, we show how these properties can be controlled by adjusting the coupling strengths and the cavity detunings. As this can be implemented with integrated optics, it provides a possible route to rugged and stable EPR sources.

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Stability results for in-phase and splay-phase states of solid-state laser arrays

Cited by 92 publications

References 29 publications

Dynamics of a Ring of Pulse-Coupled Oscillators: Group-Theoretic Approach

Dynamics of a Ring of Pulse-Coupled Oscillators: Group-Theoretic Approach

Synchronization transition of identical phase oscillators in a directed small-world network

Entanglement and the Einstein-Podolsky-Rosen paradox with coupled intracavity optical down-converters

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