Dynamics of phase oscillators with generalized frequency-weighted coupling

Xu, Can; Gao, Jian; Xiang, Hairong; Jia, Wenjing; Guan, Shuguang; Zheng, Zhigang

doi:10.1103/physreve.94.062204

Cited by 26 publications

(20 citation statements)

References 45 publications

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“…This heterogeneity induces the asymmetry in the interaction, as a recipient and a sender are not equivalent. Dynamics of such systems have been studied recently [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A role of asymmetry in linear response of globally coupled oscillator systems

Terada,

Ito,

Yoneda

et al. 2018

Preprint

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The linear response is studied in globally coupled oscillator systems including the Kuramoto model. We develop a linear response theory which can be applied to systems whose coupling functions are generic. Based on the theory, we examine the role of asymmetry introduced to the natural frequency distribution, the coupling function, or the coupling constants. A remarkable difference appears in coexistence of the divergence of susceptibility at the critical point and a nonzero phase gap between the order parameter and the applied external force. The coexistence is not allowed by the asymmetry in the natural frequency distribution but can be realized by the other two types of asymmetry. This theoretical prediction and the coupling-constant dependence of the susceptibility are numerically verified by performing simulations in N -body systems and in reduced systems obtained with the aid of the Ott-Antonsen ansatz.

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“…This heterogeneity induces the asymmetry in the interaction, as a recipient and a sender are not equivalent. Dynamics of such systems have been studied recently [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A role of asymmetry in linear response of globally coupled oscillator systems

Terada,

Ito,

Yoneda

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…In this setting, the randomness is intrinsic to the oscillators themselves rather than to the coupling between them [41][42][43][44][45][46][47][48][49]. Moreover, β ≥ 1 (β < 1) sets up a positive (negative) feedback between the coupling and the coherence of the system [50][51][52][53][54][55].…”

Section: Mathematical Model and Its Stationary Solutionsmentioning

confidence: 99%

Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators

Xu,

Tang,

Lü

et al. 2021

Preprint

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Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying a variant of the Kuramoto model, where the coupling between the phase oscillators is heterogeneous and nonlinear. In particular, the quenched disorder in the coupling strength and the intrinsic frequencies are correlated, and the coupling is extended to depend on the global rhythm of the population. We show that the interplay of these factors leads to a fascinatingly rich collective dynamics, including explosive synchronization transitions, hybrid transitions with hysteresis absence, abrupt irreversible desynchronization transitions, and tiered phase transitions with or without a vanishing onset. We develop an analytical treatment that enables us to determine the observed equilibrium states of the system, as well as to explore their asymptotic stability at various levels. Our research thus provides theoretical foundations for a number of self-organized phenomena that may be responsible for the emergence of collective rhythms in complex systems.

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“…where Ω c is the critical mean-field frequency (the imaginary part of the eigenvalue), which satisfies the balanced principal-value integral equation [25] ò w w w…”

Section: Dynamical Model and Mean-field Theorymentioning

confidence: 99%

“…Therefore, determining their stability becomes an important theoretical task. As we know, the incoherent state is neutrally stable due to the absence of eigenvalues for the linear operator in the region κ<κ c,1 , while its stability is further determined by the resonant pole calculated through analytical continuation [25]. The natural question is how the eigenspectrum for the phase-locked state appears.…”

Section: Stability Of the Phase-locked Statesmentioning

confidence: 99%

Universal phase transitions to synchronization in Kuramoto-like models with heterogeneous coupling

Boccaletti

Zheng

et al. 2019

New J. Phys.

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We reveal a class of universal phase transitions to synchronization in Kuramoto-like models with both in-and out-coupling heterogeneity. By analogy with metastable states, an oscillatory state occurs as a high-order coherent phase accompanying explosive synchronization in the system. The critical points of synchronization transition and the stationary solutions are obtained analytically, by the use of mean-field theory. In particular, the stable conditions for the emergence of phase-locked states are determined analytically, consistently with the analysis based on the Ott-Antonsen manifold. We demonstrate that the in-or out-coupling heterogeneity have influence on both the dynamical properties (eigen'spectrum) and the synchronizability of the system.

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Dynamics of phase oscillators with generalized frequency-weighted coupling

Cited by 26 publications

References 45 publications

A role of asymmetry in linear response of globally coupled oscillator systems

A role of asymmetry in linear response of globally coupled oscillator systems

Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators

Universal phase transitions to synchronization in Kuramoto-like models with heterogeneous coupling

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