Kuramoto model with additional nearest-neighbor interactions: Existence of a nonequilibrium tricritical point

Sarkar, Mrinal; Gupta, Shamik

doi:10.1103/physreve.102.032202

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…In many practical scenarios individuals may have only a limited range of interaction with others. This is taken into account in the nearest-neighbor model where the time-evolution of an oscillator is affected only by the closest neighbor [4]. This model does not cover all aspects of the limited range interaction because the nearest neighbor may be at a large phase distance.…”

Section: Introductionmentioning

confidence: 99%

Connectivity and Synchronization in Bounded Confidence Kuramoto Oscillators

Srivastava,

Bernardo,

Altafini

et al. 2024

IEEE Control Syst. Lett.

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Frequency synchronization of bounded confidence Kuramoto oscillators is analyzed. The dynamics of each oscillator is defined by the average of the phase differences with its neighbors, where any two oscillators are considered neighbors if their geodesic distance is less than a certain confidence threshold. A phase-dependent graph is defined whose nodes and edges represent the oscillators and their connections, respectively. It is studied how the connectivity of the graph influences steady-state behaviors of the oscillators. It is proved that the oscillators synchronize asymptotically if the subgraph of each partition, possibly not complete, eventually remains constant over time. Simulation results show the application of the theoretical findings also in the presence of oscillators having different natural frequencies.

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Section: Introductionmentioning

confidence: 99%

Connectivity and Synchronization in Bounded Confidence Kuramoto Oscillators

Srivastava,

Bernardo,

Altafini

et al. 2024

IEEE Control Syst. Lett.

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“…Examples are, for instance, blackouts in the power grid [2], breakdown of the internet [3], episodes of Fibromyalgia chronic pain [4] and epileptic seizures [5] in the human brain. The explosive synchronization (ES) transition is shown to emerge in networked oscillators with microscopic correlation between their frequency and network's structural property such as degree [6] and coupling strength [7], or by inclusion of inertia [8,9,10] and noise [10,11], or by the presence of a fraction of adaptively coupled oscillators [12,13,14,15,16,17], mean-field diffusion [18], traffic processes [19], the presence of nearest-neighbor competitive interaction or symmetrybreaking interaction [20] and anti-Hebbian adaptation of link weight [21].…”

Section: Introductionmentioning

confidence: 99%

Interlayer Hebbian plasticity induces first-order transition in multiplex networks

et al. 2020

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Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive interlayer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the link weight between a pair of interconnected nodes is enhanced if the two nodes are in phase. Such adaptive coupling induces an irreversible first-order transition route to synchronization accompanied with a hysteresis. We provide rigorous analytic predictions of the critical coupling strengths for the onset of synchronization and de-synchronization, and verify all our theoretical predictions by means of extensive numerical simulations.

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Kuramoto model with additional nearest-neighbor interactions: Existence of a nonequilibrium tricritical point

Cited by 2 publications

References 26 publications

Connectivity and Synchronization in Bounded Confidence Kuramoto Oscillators

Connectivity and Synchronization in Bounded Confidence Kuramoto Oscillators

Interlayer Hebbian plasticity induces first-order transition in multiplex networks

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