Synchronization of phase oscillators with heterogeneous coupling: A solvable case

@article{Paissan2008SynchronizationOP,
  title={Synchronization of phase oscillators with heterogeneous coupling: A solvable case},
  author={G. Paissan and D. Zanette},
  journal={Physica D: Nonlinear Phenomena},
  year={2008},
  volume={237},
  pages={818-828}
}
We consider an extension of Kuramoto’s model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an oscillator, Kuramoto’s theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight… Expand

Figures from this paper

Synchronization of oscillators in a Kuramoto-type model with generic coupling.
TLDR
This work presents the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. Expand
Interplay of noise and coupling in heterogeneous ensembles of phase oscillators
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same allExpand
Synchronization of phase oscillators with frequency-weighted coupling
TLDR
This paper proposes a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings, and shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Expand
Adaptive coupling induced multi-stable states in complex networks
Abstract Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics andExpand
A role of asymmetry in linear response of globally coupled oscillator systems.
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 areExpand
Rhythmic synchronization and hybrid collective states of globally coupled oscillators
TLDR
Thorough theoretical and numerical analyses indicate the presence of multiple phase transitions between different collective states, with regions of bi-stability in Globally interacting oscillators with heterogeneous couplings. Expand
Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength.
  • H. Hong
  • Physics, Medicine
  • Physical review. E
  • 2017
TLDR
The effects of the randomness on the finite-size scaling behavior of the Kuramoto model is explored, where the scaling behavior is found to be characterized by the unusual exponent ν[over ¯]=5/2. Expand
Conformist–contrarian interactions and amplitude dependence in the Kuramoto model
We derive exact formulas for the frequency of synchronized oscillations in Kuramoto models with conformist–contrarian interactions, and determine necessary conditions for synchronization to occur.Expand
The WS transform for the Kuramoto model with distributed amplitudes, phase lag and time delay
We apply the Watanabe–Strogatz (WS) transform to a generalized Kuramoto model with distributed parameters describing the amplitude of oscillation, phase lag, and time delay at each node of theExpand
Phase diagram for the Kuramoto model with van Hemmen interactions.
We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analyticallyExpand
...
1
2
...

References

SHOWING 1-10 OF 19 REFERENCES
Synchronization and clustering of phase oscillators with heterogeneous coupling
We generalize Kuramoto's theory for the synchronization transition of globally coupled phase oscillators to populations where each oscillator has a different coupling strength. We show that, beyondExpand
Biological rhythms and the behavior of populations of coupled oscillators.
  • A. Winfree
  • Mathematics, Medicine
  • Journal of theoretical biology
  • 1967
TLDR
It is proposed that self-entraining communities of this sort may exist within individual metazoan animals and plants as the basis of the observed diurnal coordination of their physiological process. Expand
A Soluble Active Rotater Model Showing Phase Transitions via Mutual Entertainment
Some analytical results are obtained for a large population of limit·cycle oscillators modelled by a set of deterministic equations 1>i = WiNK'2;/j~lsin(<pi<pj+a) (i =1,2, ... , N), where <Pi is theExpand
Clustering in globally coupled phase oscillators.
TLDR
It is found that the cluster state of the globally coupled phase oscillators is stable to the addition of weak stochastic noise, and marginal states are observed, characterized by a continuum of marginally stable limit trajectories. Expand
Cooperative action of coherent groups in broadly heterogeneous populations of interacting chemical oscillators.
TLDR
The experiments show that complex collective signals are generated by this system through spontaneous emergence and joint operation of coherently acting groups representing hierarchically organized resonant clusters, suggesting that some forms of internal self-organization, characteristic for complex multiagent systems, are already possible in simple chemical systems. Expand
Theory of collective firing induced by noise or diversity in excitable media.
TLDR
This work develops a theory for the emergence of collective firings in nonidentical excitable systems subject to noise and shows that the mechanism for collective firing is generic: it arises from degradation of entrainment originated either by noise or by diversity. Expand
Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions.
  • Daido
  • Physics, Medicine
  • Physical review letters
  • 1992
It is numerically shown that there may be a new type of ordered state (in some sense glassy) in far-from-equilibrium systems which can be identified with a large population of coupled limit-cycleExpand
Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements
Abstract A Network of chaotic elements is investigated with the use of globally coupled maps. A simple coding of many attractors with clustering is shown. Through the coding, the attractors areExpand
Condensation in globally coupled populations of chaotic dynamical systems
The condensation transition, leading to complete mutual synchronization in large populations of globally coupled chaotic R\"ossler oscillators, is investigated. Statistical properties of thisExpand
...
1
2
...