Explosive transitions to synchronization in networks of phase oscillators

Leyva, I.; Navas, Adrián; Sendiña‐Nadal, Irene; Almendral, Juan A.; Buldú, Javier M.; Zanin, Massimiliano; Papo, David; Boccaletti, Stefano

doi:10.1038/srep01281

Cited by 109 publications

(117 citation statements)

References 18 publications

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“…5(f), as the coupling strength K is varied, the order parameter R of the phase oscillators interconnected by the minimal ES network exhibits a sudden hysteretic change, associated to a discontinuous phase transition, whereas the system with a unimodal frequency distribution undergoes a continuous phase transition [5]. This discontinuous phase transition, also known as "explosive synchronisation", has been studied in the literature [18][19][20][21], also in the case of adaptive networks [22,23], revealing that the correlation between natural frequencies and the node degree, as shown in Fig. 4(d), can induce this phenomenon.…”

Section: Emergence Of Minimal Networkmentioning

confidence: 99%

Heterogeneity induces emergent functional networks for synchronization

2015

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We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We demonstrate that increasing heterogeneity among the nodes in state-dependent networks of phase oscillators causes a differentiation in the activation probabilities of the links. This, in turn, yields the formation of hubs associated to nodes with larger distances from the average frequency of the ensemble. Our generic local evolutionary strategy can be used to solve a wide range of synchronization and control problems.

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Section: Emergence Of Minimal Networkmentioning

confidence: 99%

Heterogeneity induces emergent functional networks for synchronization

2015

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“…Many works addressed the latter kind of question recently, see e.g. references [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For interesting recent works that highlight the special interplay between dynamics and network structure in neuronal systems, we refer to [27,28].…”

Section: Introductionmentioning

confidence: 99%

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

et al. 2014

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Abstract. We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the selfoscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.

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“…In their work, Jesus et al [22] interestingly considered degree-frequency correlated scale-free (SF) network topology and reported a first order transition to synchrony or so called explosive synchronization (ES) for the first time in Kuramoto paradigm which is characterized by a sharp jump of the order parameter [13] as the system passes from incoherence to synchronization [23,24]. Considering similar degree-frequency correlated SF networks, Peron et al [25] determined analytical expression of critical coupling for ES using mean field approach [26].…”

Section: Introductionmentioning

confidence: 99%

Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

et al. 2017

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We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdős-Rényi (ER) networks in detail. Depending on the degree distribution exponent (γ) of SF networks and phase-frustration parameter, the population undergoes from first order transition (explosive synchronization (ES)) to second order transition and vice versa. In ER networks transition is always second order irrespective of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self consistent equations considering the vanishing order parameter limit.

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Explosive transitions to synchronization in networks of phase oscillators

Cited by 109 publications

References 18 publications

Heterogeneity induces emergent functional networks for synchronization

Heterogeneity induces emergent functional networks for synchronization

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

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