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Independent dimensional phase transition on a two-dimensional Kuramoto model with matrix coupling [article]

Chongzhi Wang, Haibin Shao, Dewei Li
2021 arXiv   pre-print
As a natural extension of the scalar coupling befitting for the one-dimensional case, we take a tentative step in studying numerically and theoretically the coupling mechanism of 2×2 real matrices on two-dimensional  ...  One of the features stemmed from this new mechanism is that the matrix coupling enables the two dimensions of the oscillators to separate their transitions to either synchronization or desynchronization  ...  FIG. 1 illustrates the mechanism of the two-dimensional Kuramoto model with the matrixcoupling; one should notice that the dynamics on one dimension of a specific oscillator is taking direct influences  ... 
arXiv:2108.11652v1 fatcat:lheddelmd5depauqrujwwitqjy

Explosive higher-order Kuramoto dynamics on simplicial complexes [article]

Ana P. Millán, Joaquín J. Torres, Ginestra Bianconi
2020 arXiv   pre-print
We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.  ...  Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on.  ...  S − 5. we coupled these two independent dynamics is inspired by the coupling of the dynamics of multiplex Kuramoto dynamics in Ref. [28] .  ... 
arXiv:1912.04405v3 fatcat:ocx6qsw4izg2tda2anzaxpgeeu

Continuous versus Discontinuous Transitions in the D -Dimensional Generalized Kuramoto Model: Odd D is Different

Sarthak Chandra, Michelle Girvan, Edward Ott
2019 Physical Review X  
Partly based on this motivation, as well as on relevance to the classical, mean-field, zero-temperature Heisenberg model with quenched site disorder, in this paper we study the Kuramoto model generalized  ...  The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large  ...  Phase transitions for the standard two-dimensional Kuramoto model from theory (see Ref.  ... 
doi:10.1103/physrevx.9.011002 fatcat:mq5arzl7xzc57aqlisphqsfycq

Geometry, Topology and Simplicial Synchronization [article]

Ana Paula Millán, Juan G. Restrepo, Joaquín J. Torres, Ginestra Bianconi
2022 arXiv   pre-print
On its turn simplicial topology is shown to determine the dynamical properties of the higher-order Kuramoto model.  ...  This theoretical result is here verified on the Network Geometry with Flavor simplicial complex generative model displaying emergent hyperbolic geometry.  ...  Kuramoto model we explore the phase diagram of the normalized Kuramoto model on networks with finite spectral dimension [32] .  ... 
arXiv:2105.00943v2 fatcat:dsqrers53rekvi6onzhr6u6mvq

Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach

Rafael S. Pinto, Alberto Saa
2015 Physical Review E  
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization.  ...  Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer  ...  The Kuramoto model is known to exhibit a second order phase transition from the incoherent to the synchronized regime at a critical value λ c of the coupling strength.  ... 
doi:10.1103/physreve.92.062801 pmid:26764738 fatcat:aevzuyztb5ernib2adwn3srywa

Higher-order simplicial synchronization of coupled topological signals [article]

Reza Ghorbanchian, Juan G. Restrepo, Joaquín J. Torres, Ginestra Bianconi
2021 arXiv   pre-print
a discontinuous phase transition.  ...  We show that coupling between signals defined on nodes and links leads to explosive topological synchronization in which phases defined on nodes synchronize simultaneously to phases defined on links at  ...  Specifically we focus on the coupling of the traditional Kuramoto model [Eq. (2) ] to a higher-order topological Kuramoto model defined for phases associated to the links [Eq. (6) ].  ... 
arXiv:2011.00897v2 fatcat:vkuuk5g3f5eshgbknb3v3uxwlq

Synchronization in disordered oscillatory media: a nonequilibrium phase transition for driven-dissipative bosons [article]

John P. Moroney, Paul R. Eastham
2021 arXiv   pre-print
We show that a lattice of phase oscillators with random natural frequencies, described by a generalization of the nearest-neighbor Kuramoto model with an additional cosine coupling term, undergoes a phase  ...  We derive phase diagrams that classify the desynchronized and synchronized states that exist in both one and two dimensions.  ...  With all-to-all couplings the Kuramoto model undergoes a phase transition, from a desynchronized state at weak coupling to a globally synchronized state at strong coupling.  ... 
arXiv:2101.05776v2 fatcat:4d5hw224wfhqheo2erbji25p7q

Desynchronization transitions in nonlinearly coupled phase oscillators

Oleksandr Burylko, Arkady Pikovsky
2011 Physica D : Non-linear phenomena  
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter.  ...  We demonstrate that for small ensembles it is typically mediated by stable cluster states, that disappear with creation of heteroclinic cycles, while for a larger number of oscillators a direct transition  ...  Most popular is the Kuramoto model of sine-coupled phase oscillators, or its extension, the Kuramoto-Sakaguchi model [8] .  ... 
doi:10.1016/j.physd.2011.05.016 fatcat:dtx3o7wlxfckpc7oojidiazwh4

Transition to Synchrony in a Three-Dimensional Swarming Model with Helical Trajectories [article]

Chunming Zheng, Ralf Toenjes, Arkady Pikovsky
2020 arXiv   pre-print
We investigate the transition from incoherence to global collective motion in a three dimensional swarming model of agents with helical trajectories, subject to noise and global coupling.  ...  Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found, that alignment of the velocities occurs for arbitrary small attractive coupling.  ...  In contrast to the two dimensional Kuramoto model, the critical coupling strength goes to zero when D goes to zero regardless of the frequency distribution.  ... 
arXiv:2007.07612v1 fatcat:5p2xz4myy5ae3pk4kp2hx4pe3e

Kuramoto dynamics in Hamiltonian systems

Dirk Witthaut, Marc Timme
2014 Physical Review E  
Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds  ...  The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony.  ...  On one given torus, i.e., for one value of I , the dynamics of the phaseṡ φ j = ω j + LI + N =1 2I K ,j sin(φ − φ j ), (8) equals that of the original Kuramoto model (1) with a rescaled coupling matrix  ... 
doi:10.1103/physreve.90.032917 pmid:25314514 fatcat:5dctxcyvgje5dbipvx3wg2ye2m

On the critical coupling strength for Kuramoto oscillators

Florian Dorfler, Francesco Bullo
2011 Proceedings of the 2011 American Control Conference  
Finally, we present the first explicit necessary and sufficient condition on the critical coupling strength to achieve synchronization in the finite-dimensional Kuramoto model for an arbitrary distribution  ...  It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronization occurs. This paper features three contributions.  ...  THE KURAMOTO MODEL OF COUPLED OSCILLATORS A classic model for the synchronization of coupled oscillators is due to Kuramoto [1] .  ... 
doi:10.1109/acc.2011.5991303 fatcat:hd5gqgfj35aivhhnk6zf3xbydy

Synchronization of frustrated phase oscillators in the small-world networks [article]

Esmaeil Mahdavi, Mina Zarei, Farhad Shahbazi
2022 arXiv   pre-print
We also observe abrupt phase transition with hysteresis at some values of phase shifts in small-world networks, signs of an explosive phase transition.  ...  We numerically study the synchronization of an identical population of Kuramoto-Sakaguchi phase oscillators in Watts-Strogatz networks.  ...  One of the most studied models for phase synchronization is the Kuramoto model, where the synchronization mechanism is due to a nonlinear coupling associated with the Sinus of the phase difference between  ... 
arXiv:2205.08849v1 fatcat:sp2jj7pckzfpbexv5gnrc3jjuy

Synchronization in cilia carpets and the Kuramoto model with local coupling: breakup of global synchronization in the presence of noise [article]

Anton Solovev, Benjamin M. Friedrich
2021 arXiv   pre-print
Our theoretical work establishes a link between the two-dimensional Kuramoto model of phase oscillators with symmetric oscillator coupling and detailed models of biological oscillators with asymmetric,  ...  We characterize stochastic transitions between synchronized and disordered dynamics, which generalizes the notion of phase slips in pairs of coupled noisy phase oscillators.  ...  Kuramoto model with nearest-neighbor coupling on a one-dimensional ring We consider a one-dimensional chain of N coupled phase oscillators with periodic boundary conditions.  ... 
arXiv:2109.08639v1 fatcat:j4hhhrztkzfublep55dhihkace

On the Critical Coupling for Kuramoto Oscillators [article]

Florian Dorfler, Francesco Bullo
2011 arXiv   pre-print
It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronization occurs. This paper features four contributions.  ...  Third, we present the first explicit necessary and sufficient condition on the critical coupling to achieve synchronization in the finite-dimensional Kuramoto model for an arbitrary distribution of the  ...  For K = K critical , we know from [38, 3] that phase-locked equilibria have a zero eigenvalue with a two-dimensional Jacobian block, and thus synchronization cannot occur.  ... 
arXiv:1011.3878v2 fatcat:tdet5eb3i5dktbklawrdmilqwu

Model reduction for Kuramoto models with complex topologies

Edward J. Hancock, Georg A. Gottwald
2018 Physical review. E  
However, for the Kuramoto model - the most widely used model of coupled oscillators - this goal has remained surprisingly challenging, in particular for finite-size networks.  ...  Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology.  ...  One example, already discussed in [9] , is the Kuramoto model with a unimodal frequency distribution, where the transition to synchronisation is a second-order phase transition [11, 17] , and not all  ... 
doi:10.1103/physreve.98.012307 pmid:30110852 fatcat:wonwnpenfbarlfw2kglsls2uhu
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