Synchronization patterns in geometrically frustrated rings of relaxation oscillators

Goldstein, Daniel E.; Giver, Michael; Chakraborty, Bulbul

doi:10.1063/1.4936246

Cited by 8 publications

(5 citation statements)

References 30 publications

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“…When a group of N identical oscillators are arranged in a ring such that each oscillator is coupled to its two neighbors, the simplest group of resulting oscillator states are splay states where each pair of oscillators is separated by a constant phase difference (2πk=N), yielding an integral number (k) of phase rotations around the ring (2πk) (34). However, a splay state with perfectly antiphase synchronization between neighboring oscillators is inherently impossible when an odd number of HNDs are configured into a ring, leading to a geometrically frustrated system (37). Experimentally, we observe complex phase dynamics when HNDs are arranged in a three-oscillator ring structure, the smallest of frustrated geometries (Fig.…”

Section: Resultsmentioning

confidence: 99%

Coupled oscillation and spinning of photothermal particles in Marangoni optical traps

Kim

Sundaram

Kang

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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Cyclic actuation is critical for driving motion and transport in living systems, ranging from oscillatory motion of bacterial flagella to the rhythmic gait of terrestrial animals. These processes often rely on dynamic and responsive networks of oscillators—a regulatory control system that is challenging to replicate in synthetic active matter. Here, we describe a versatile platform of light-driven active particles with interaction geometries that can be reconfigured on demand, enabling the construction of oscillator and spinner networks. We employ optically induced Marangoni trapping of particles confined to an air–water interface and subjected to patterned illumination. Thermal interactions among multiple particles give rise to complex coupled oscillatory and rotational motions, thus opening frontiers in the design of reconfigurable, multiparticle networks exhibiting collective behavior.

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Section: Resultsmentioning

confidence: 99%

Coupled oscillation and spinning of photothermal particles in Marangoni optical traps

Kim

Sundaram

Kang

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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“…We specify the analysis method. In this study, we focus on the phase difference of the oscillators [26][27][28][29]. We explain with Fig.…”

Section: Resultsmentioning

confidence: 99%

Emergence of long-term rhythmicity within a frustrated triangle oscillator-network

Matsushima,

Ueno,

Kamiya

et al. 2019

Preprint

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“…It has been understood that the onset of synchronous behaviour can be affected by the local connectivity and correlations among the nodes [34], and global features captured by the network's spectral dimension [35]. The nature of synchronisation transition can depend on the process' sensitivity to the sign of interactions, time delay, and the frustration effects causing new phenomena [36][37][38][39][40][41]. Furthermore, the presence of higherorder interactions are shown to induce an abrupt desynchronisation, depending on the dimension of the dynamical variable, and the range of couplings [9,10].…”

Section: Introductionmentioning

confidence: 99%

Hysteresis and synchronization processes of Kuramoto oscillators on high-dimensional simplicial complexes with the competing simplex-encoded couplings

Chutani,

Tadic,

Gupte

2021

Preprint

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Recent studies of dynamic properties in complex systems point out the profound impact of hidden geometry features known as simplicial complexes, which enable geometrically conditioned many-body interactions. Studies of collective behaviours on the controlled-structure complexes can reveal the subtle interplay of geometry and dynamics. Here, we investigate the phase synchronisation (Kuramoto) dynamics under the competing interactions embedded on 1-simplex (edges) and 2-simplex (triangles) faces of a homogeneous 4-dimensional simplicial complex. Its underlying network is a 1-hyperbolic graph with the assortative correlations among the node's degrees and the spectral dimension that exceeds d s = 4. By solving numerically the set of coupled equations for the phase oscillators associated with the network nodes, we determine the time-averaged system's order parameter to characterise the synchronisation level. In the absence of higher interactions, the complete synchrony is continuously reached with the increasing positive pairwise interactions (K 1 > 0), and a partial synchronisation for the negative couplings (K 1 < 0) with no apparent hysteresis. Similar behaviour occurs in the degree-preserved randomised network. In contrast, the synchronisation is absent for the negative pairwise coupling in the entirely random graph and simple scale-free networks. Increasing the strength K 2 = 0 of the triangle-based interactions gradually hinders the synchronisation promoted by pairwise couplings, and the non-symmetric hysteresis loop opens with an abrupt desynchronisation transition towards the K 1 < 0 branch. However, for substantial triangle-based interactions, the frustration effects prevail, preventing the complete synchronisation, and the abrupt transition disappears. These findings shed new light on the mechanisms by which the high-dimensional simplicial complexes in natural systems, such as human connectomes, can modulate their native synchronisation processes.

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Synchronization patterns in geometrically frustrated rings of relaxation oscillators

Cited by 8 publications

References 30 publications

Coupled oscillation and spinning of photothermal particles in Marangoni optical traps

Coupled oscillation and spinning of photothermal particles in Marangoni optical traps

Emergence of long-term rhythmicity within a frustrated triangle oscillator-network

Hysteresis and synchronization processes of Kuramoto oscillators on high-dimensional simplicial complexes with the competing simplex-encoded couplings

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