Repulsive Synchronization in an Array of Phase Oscillators

Tsimring, Lev S.; Rulkov, Nikolai F.; Larsen, Michael L.; Gabbay, Michael

doi:10.1103/physrevlett.95.014101

Cited by 121 publications

(78 citation statements)

References 20 publications

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“…The formula (22) also applies to synchronized systems with nontrivial network topologies, such as those considered in [4,5,14]; it is necessary only that (a ij ) be symmetric. Equation (21) can be integrated to obtain a nontrivial constant of the motion:…”

Section: Synchronized Frequencymentioning

confidence: 99%

Conformist–contrarian interactions and amplitude dependence in the Kuramoto model

Lohe¹

2014

Phys. Scr.

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Abstract. 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. Numerical computations show that for certain parameters repulsive nodes behave as conformists, and that in other cases attractive nodes can display frustration, being neither conformist nor contrarian. The signs of repulsive couplings can be placed equivalently outside the sum, as proposed in Phys. Rev. Lett. 106 (2011) 054102, or inside the sum as in Phys. Rev. E 85 (2012) 056210, but the two models have different characteristics for small magnitudes of the coupling constants. In the latter case we show that the distributed coupling constants can be viewed as oscillator amplitudes which are constant in time, with the property that oscillators of small amplitude couple only weakly to connected nodes. Such models provide a means of investigating the effect of amplitude variations on synchronization properties.

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Section: Synchronized Frequencymentioning

confidence: 99%

Conformist–contrarian interactions and amplitude dependence in the Kuramoto model

Lohe¹

2014

Phys. Scr.

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“…Therefore, our primary aim was to examine PAT volumes in patients with chronic MDD by cardiac magnetic resonance imaging (33), and to relate PAT volumes to adrenal gland volumes, a proxy parameter for HPAS activation. Our main hypothesis was that chronic MDD is associated with higher PAT volumes and worse metabolic parameters compared to patients with acute MDD and healthy controls.…”

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confidence: 99%

Pericardial adipose tissue and the metabolic syndrome is increased in patients with chronic major depressive disorder compared to acute depression and controls

Kahl

Herrmann

Stubbs

et al. 2017

Progress in Neuro-Psychopharmacology and Biological Psychiatry

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“…Whereas, repulsive couplings have been shown to affect dynamical evolution of nonlinear units in different ways. The repulsive couplings may either destroy a synchronized state leading to the incoherent evolution 22 or lead to an emergence of new synchronization regimes in addition to the multistability phenomenon 23 . An emergence of the chimera state under attractive and repulsive couplings in a globally coupled monoplex network has already been reported 24 .…”

Section: Introductionmentioning

confidence: 99%

Is repulsion good for the health of chimeras?

Jalan

Ghosh

Patra

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Yes! Very much so.A chimera state refers to the coexistence of a coherent-incoherent dynamical evolution of identically coupled oscillators. We investigate the impact of multiplexing of a lyer having repulsively coupled oscillators on occurrence of chimeras in the layer having attractively coupled identical oscillators. We report that there exists an enhancement in the appearance of chimera state in one layer of multiplex network in the presence of repulsive coupling in the other layer. Furthermore, we show that a small amount of inhibition or repulsive coupling in one layer is sufficient to yield chimera state in another layer by destroying its synchronized behavior. These results can be used to get insight into dynamical behaviors of those systems where both attractive and repulsive coupling exist among their constituents. In 1975, Kuramoto had introduced a mathematical model for nonidentical, nonlinear phase oscillators which exhibits a convergence to a global synchrony at a critical coupling value. In 2002, Kuramoto demonstrated that identical phase oscillators can show coexistence of coherent and incoherent dynamics under certain special conditions. Later, Abrams and Strogatz, christened this dynamical state as chimera state and provided a detailed description about special conditions required for its emergence. Since then, chimera remains an exotic phenomenon with ambiguities. Initially, non-local, non-global topology was stated to be a prerequisite for the emergence of the chimera state. However, subsequent investigations presented an appearance of the chimera state for both local and global couplings. Furthermore, multiplex framework which incorporate various types of interactions between the same pair of nodes as different layers, provide a better portrayal of complex natural networks. Here we consider a multiplex network with each layer having identical coupling architecture but not necessarily identical nature of the couplings. Particularly, we consider attractive and repulsive coupling among dynamical units and show that by keeping network architecture same, coupling in one layer have profound impact on the occurrence of chimera in another layer in multiplex networks. This investigation is crucial for many different complex systems possessing different types of coupling, particularly attractive and repulsive coupling among the same units. For instance, the a) Electronic mail: sarikajalan9@gmail.com b) Electronic mail: sapta15@gmail.com brain has inhibitory and excitatory neurons representing repulsive and attractive couplings, respectively. Studies on the impact of inhibition on the emergence of chimera state in the multiplex framework will be useful for a better understanding of such complex systems in different conditions.

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Repulsive Synchronization in an Array of Phase Oscillators

Cited by 121 publications

References 20 publications

Conformist–contrarian interactions and amplitude dependence in the Kuramoto model

Conformist–contrarian interactions and amplitude dependence in the Kuramoto model

Pericardial adipose tissue and the metabolic syndrome is increased in patients with chronic major depressive disorder compared to acute depression and controls

Is repulsion good for the health of chimeras?

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