Explosive synchronization dependence on initial conditions: The minimal Kuramoto model

Bayani, Atiyeh; Jafari, Sajad; Azarnoush, Hamed; Nazarimehr, Fahimeh; Boccaletti, Stefano; Perc, Matjaž

doi:10.1016/j.chaos.2023.113243

Cited by 26 publications

(5 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Step 5 Give the reference signal of the nodes s * and choose f * (s * , ξ * , t) = [1, 1] T . At the same time, the auxiliary reference tracking target (ARTT) of the links is chosen as Equation (7).…”

Section: Simulation Examplementioning

confidence: 99%

“…Complex dynamical networks (CDNs) have received a lot of attention due to their wide application in transportation networks, telephone networks, internet networks, and many other real networks [1]. As a typical collective behavior exhibited in CDNs, synchronization has been seen as one of the most significant dynamical behaviors, and many interesting results have been reported, such as [2][3][4][5][6][7]. For example, in [7,8], the effect of the coupling strength between nodes and links on synchronization is investigated.…”

Section: Introductionmentioning

confidence: 99%

“…As a typical collective behavior exhibited in CDNs, synchronization has been seen as one of the most significant dynamical behaviors, and many interesting results have been reported, such as [2][3][4][5][6][7]. For example, in [7,8], the effect of the coupling strength between nodes and links on synchronization is investigated. It is shown that scintillating coupling enhances the synchronization of nodes in the network as well as how to determine the critical coupling strength.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

Zhao,

Wang,

Gao

et al. 2023

Entropy

View full text Add to dashboard Cite

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network’s topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

show abstract

Section: Simulation Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

Zhao,

Wang,

Gao

et al. 2023

Entropy

View full text Add to dashboard Cite

show abstract

“…Finally, it is found that the anti-phase synchronization between two pendulums is achieved by the tiny vibrations propagated by the beam, that is, by beam coupling [ 65 ]. In recent years, there are more and more research projects on how to apply the synchronization phenomenon to various fields, such as nonlinear systems [ 66 , 67 , 68 ] and complex network synchronization behavior [ 69 , 70 , 71 , 72 ].…”

Section: Introductionmentioning

confidence: 99%

Heat-Driven Synchronization in Coupled Liquid Crystal Elastomer Spring Self-Oscillators

Zhang

et al. 2023

Polymers

View full text Add to dashboard Cite

Self-oscillating coupled machines are capable of absorbing energy from the external environment to maintain their own motion and have the advantages of autonomy and portability, which also contribute to the exploration of the field of synchronization and clustering. Based on a thermally responsive liquid crystal elastomer (LCE) spring self-oscillator in a linear temperature field, this paper constructs a coupling and synchronization model of two self-oscillators connected by springs. Based on the existing dynamic LCE model, this paper theoretically reveals the self-oscillation mechanism and synchronization mechanism of two self-oscillators. The results show that adjusting the initial conditions and system parameters causes the coupled system to exhibit two synchronization modes: in-phase mode and anti-phase mode. The work conducted by the driving force compensates for the damping dissipation of the system, thus maintaining self-oscillation. The phase diagrams of different system parameters are drawn to illuminate the self-oscillation and synchronization mechanism. For weak interaction, changing the initial conditions may obtain the modes of in-phase and anti-phase. Under conditions of strong interactions, the system consistently exhibits an in-phase mode. Furthermore, an investigation is conducted on the influence of system parameters, such as the LCE elastic coefficient and spring elastic coefficient, on the amplitudes and frequencies of the two synchronization modes. This study aims to enhance the understanding of self-oscillator synchronization and its potential applications in areas such as energy harvesting, power generation, detection, soft robotics, medical devices and micro/nanodevices.

show abstract

“…-Synchronisation (injection locking) of oscillators to an external forcing (injection signal) of widely different waveforms is often used to provide means for communicating among oscillators or linking between oscillators and their surrounding environment. In many branches of science and engineering, methods for efficient synchronisation, including explosive synchronisation [1], have been developed in recent years because synchronisability plays a prominent role in functioning of engineered systems and even in the social sciences [2]. The synchronisability is measured by the width of the Arnold tongue (cf.…”

mentioning

confidence: 99%

Maximisation of synchronisability under low injection power

Tanaka,

Yabe,

Suga

et al. 2024

EPL

View full text Add to dashboard Cite

Synchronisability of limit cycle oscillators has been measured by the width of the synchronous frequency band, known as the Arnold tongue, concerning external forcing.We clarify a fundamental limit on maximizing this synchronisability within a specified extra low power budget, which underlies an important and ubiquitous problem in nonlinear science related to an efficient synchronisation of weakly forced nonlinear oscillators.In this letter, injection-locked Class-E oscillators are considered as a practical case study, and we systematically analyse their power consumption;our observations demonstrate the independence of power consumption in the oscillator from power consumption in the injection circuit and verify the dependency of power consumption in the oscillator solely on its oscillation frequency.These systematic observations, followed by the mathematical optimisation establish the existence of a fundamental limit on synchronisability, validated through systematic circuit simulations.The results offer insights into the energetics of synchronisation for a specific class of injection-locked oscillators.

show abstract

Explosive synchronization dependence on initial conditions: The minimal Kuramoto model

Cited by 26 publications

References 27 publications

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

Heat-Driven Synchronization in Coupled Liquid Crystal Elastomer Spring Self-Oscillators

Maximisation of synchronisability under low injection power

Contact Info

Product

Resources

About