One node driving synchronisation

Wang, Chengwei; Grebogi, Celso; Baptista, Murilo S.

doi:10.1038/srep18091

Cited by 5 publications

(5 citation statements)

References 37 publications

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“…The scheme has been exhaustively tested with numerical simulations and it has always resulted in an enhancement in the global synchronization properties of the system. Our main conclusion is that the optimal subset C, in the sense that will be properly define in Section III, should consist in the nodes i such that |Ω−ω i | is maximal, a result which is indeed in agreement with some recent related works 13,14,34 , and that might shed some light on the evolution and structure of natural systems for which global synchronization is a desired property. Despite our analysis is explicitly done for the Ω > 0 case with symmetric distributions g(ω), we will show that the optimization criterion of maximizing |Ω − ω i | for choosing the subset C of forced nodes is valid for more general cases as well.…”

Section: Introductionsupporting

confidence: 83%

Optimal global synchronization of partially forced Kuramoto oscillators

Clímaco

Saa

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies ω i , such that a fraction of them is subject to an external periodic force with frequency Ω, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that |ω i − Ω| is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization are desired properties. Some properties of the optimal forced networks and its relation to recent results in the literature are also discussed.We consider here the dynamics of a large number of interacting Kuramoto oscillators. Each oscillator has its own natural frequency ω i , which is assumed to be a random variable, and the interactions among them are associated with the edges of a random network. Despite of being essentially a random system, there are plenty of robust results obtained from this kind of model which have proven to be relevant in many different areas. This is the case, for instance, of synchronization phenomena, see 1 and 2 for comprehensive reviews on the subject. Here, we are concerned with one of the main variations of the network of Kuramoto oscillators, the case where some of the oscillators are subject to an external periodically driven force with frequency Ω. By exploring a recently proposed analytical approach, we introduce an optimization scheme for the onset of the so-called global synchronization in the system, a regime where all oscillators rigidly rotate, forming a compact swarm, in the same pace of the external force, with frequency Ω. We show that the best global synchronization properties correspond to the case where the set of forced oscillators is chosen to be those ones such that the value of |ω i −Ω| is maximal. Our results may help to understand the evolution and structure of natural systems with many interacting agents for which global synchronization plays an important dynamical role.

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Section: Introductionsupporting

confidence: 83%

Optimal global synchronization of partially forced Kuramoto oscillators

Clímaco

Saa

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In order to get insight into the general behavior of the system we present a set of simulations for the following networks: For the fully connected networks the critical value λ c for the onset of synchronization can be estimated when N → ∞ as λ c = 2a 2/π ≈ 1.6. For finite networks the calculation of λ c can be performed numerically (see, for example, [31]) and we have checked that λ c = 1.6 is a good approximation even for N = 100 and for the other topologies we used. Full synchronization occurs only for larger values of λ and we define λ f as the value where r = 0.95 andψ < 10 −2 .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Another interesting choice would be to pick them according to their natural frequencies ω i . For finite systems the oscillator with the largest frequency determines the spontaneous synchronization of the system [31] and forcing the fastest nodes might also result in interesting dynamics.…”

Section: Discussionmentioning

confidence: 99%

Global synchronization of partially forced Kuramoto oscillators on networks

Moreira

Aguiar

2019

Physica A: Statistical Mechanics and its Applications

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We study the synchronization of Kuramoto oscillators on networks where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force if its intensity is sufficiently large. Our goal is to understand the conditions for global synchronization as a function of the fraction of nodes being forced and how these conditions depend on network topology, strength of internal couplings and intensity of external forcing. Numerical simulations show that the force required to synchronize the network with the external drive increases as the inverse of the fraction of forced nodes. However, for a given coupling strength, synchronization does not occur below a critical fraction, no matter how large is the force. Network topology and properties of the forced nodes also affect the critical force for synchronization. We develop analytical calculations for the critical force for synchronization as a function of the fraction of forced oscillators and for the critical fraction as a function of coupling strength. We also describe the transition from synchronization with the external drive to spontaneous synchronization.

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“…One of the most prominent and extensively studied network models for analyzing the stability of synchronization in complex networks is the Kuramoto network model [41][42][43][44] , which has also been generalized to higher order. Through linearization, the stability of the complete synchronous mode in the higherorder Kuramoto network is associated with the properties of the generalized Laplacian 40,45 .…”

Section: Introductionmentioning

confidence: 99%

The complementary contribution of each order topology into the synchronization of multi-order networks

Ren,

Lei,

Grebogi

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Higher-order interactions improve our capability to model real-world complex systems ranging from physics and neuroscience to economics and social sciences. There is great interest nowadays in understanding the contribution of higher-order terms to the collective behavior of the network. In this work, we investigate the stability of complete synchronization of complex networks with higher-order structures. We demonstrate that the synchronization level of a network composed of nodes interacting simultaneously via multiple orders is maintained regardless of the intensity of coupling strength across different orders. We articulate that lower-order and higher-order topologies work together complementarily to provide the optimal stable configuration, challenging previous conclusions that higher-order interactions promote the stability of synchronization. Furthermore, we find that simply adding higher-order interactions based on existing connections, as in simple complexes, does not have a significant impact on synchronization. The universal applicability of our work lies in the comprehensive analysis of different network topologies, including hypergraphs and simplicial complexes, and the utilization of appropriate rescaling to assess the impact of higher-order interactions on synchronization stability.

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One node driving synchronisation

Cited by 5 publications

References 37 publications

Optimal global synchronization of partially forced Kuramoto oscillators

Optimal global synchronization of partially forced Kuramoto oscillators

Global synchronization of partially forced Kuramoto oscillators on networks

The complementary contribution of each order topology into the synchronization of multi-order networks

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