Multi-population phase oscillator networks with higher-order interactions

Bick, Christian; Böhle, Tobias; Kuehn, Christian

doi:10.1007/s00030-022-00796-x

Cited by 14 publications

(10 citation statements)

References 52 publications

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“…Also, numerous other variations were taken into account, including phase oscillators under higher-order interaction and planar oscillators [16][17][18][19][20][21][22][23]. In addition, chimera states have been ceaselessly studied by adopting three-and multi-population networks as underlying system topology [24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks

Lee,

Krischer

2023

J. Phys. A: Math. Theor.

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Chimera dynamics, an intriguing phenomenon of coupled oscillators, is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto–Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an M-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in Tanaka (2014 New. J. Phys. 16 023016) where the macroscopic dynamics of the system was studied using the extended Watanabe–Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.

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Section: Introductionmentioning

confidence: 99%

Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks

Lee,

Krischer

2023

J. Phys. A: Math. Theor.

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“…Indeed, nonpairwise phase coupling terms between more than two oscillator phases have been associated with phase oscillator dynamics on hypergraphs (Battiston et al 2020;; these can arise for example through higher-order phase reductions of additively coupled systems (e.g., León and Pazó 2019) or first-order phase reductions of oscillators with generic nonlinear coupling (Ashwin et al 2016b). So far, many phase oscillator networks with higher-order interactions that have been considered were ad-hoc, for example, by generalizing the Kuramoto model to hypergraphs (see, e.g., Skardal and Arenas 2020;Bick et al 2022). By contrast, our results provide a natural family of hypergraphs together with phase interaction functions that describe the synchronization behavior of an (unreduced) nonlinear oscillator network.…”

Section: Introductionmentioning

confidence: 81%

Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude

Bick,

Böhle,

Kuehn

2024

J Nonlinear Sci

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Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction—the reduction of the dynamics onto an invariant torus—captures the emergence of collective dynamical phenomena, such as synchronization. While a first-order approximation of the dynamics on the torus may be appropriate in some situations, higher-order phase reductions become necessary, for example, when the coupling strength increases. However, these are generally hard to compute and thus they have only been derived in special cases: This includes globally coupled Stuart–Landau oscillators, where the limit cycle of the uncoupled nonlinear oscillator is circular as the amplitude is independent of the phase. We go beyond this restriction and derive second-order phase reductions for coupled oscillators for arbitrary networks of coupled nonlinear oscillators with phase-dependent amplitude, a scenario more reminiscent of real-world oscillations. We analyze how the deformation of the limit cycle affects the stability of important dynamical states, such as full synchrony and splay states. By identifying higher-order phase interaction terms with hyperedges of a hypergraph, we obtain natural classes of coupled phase oscillator dynamics on hypergraphs that adequately capture the dynamics of coupled limit cycle oscillators.

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“…Graphs focus on analyzing relationships between pairs of objects. The simple combinatorial structure allows graph models to be more interpretable and flexible [72]. In addition to graphs, the simplicial complex is another method used to represent interactions among subjects.…”

Section: Discussionmentioning

confidence: 99%

Graph neural networks for image‐guided disease diagnosis: A review

et al. 2023

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Medical imaging is playing an increasingly crucial role in disease diagnosis. Numerous deep learning-based methods have been developed for imageguided automatic disease diagnosis. Most of the methods have harnessed conventional convolutional neural networks, which are directly applied in the regular image domain. However, some irregular spatial patterns revealed in medical images are also critical to disease diagnosis, since they can describe latent relations in different image regions of a subject (e.g., different focal lesions in an image) or between different groups (e.g., Alzheimer's disease and healthy control). Therefore, how to exploit and analyze irregular spatial patterns and their relations has become a research challenge in the field of imageguided disease diagnosis. To address this challenge, graph neural networks (GNNs) are proposed to perform the convolution operation on graphs. Graphs can naturally represent irregular spatial structures. Because of their ability to aggregate node features, edge features, and graph structure information to capture and learn hidden spatial patterns in irregular structures, GNN-based algorithms have achieved promising results in the detection of various diseases. In this paper, we introduce commonly used GNN-based algorithms and systematically review their applications to disease diagnosis. We summarize the workflow of GNN-based applications in disease diagnosis, ranging from localizing the regions of interest and edge construction to modeling. Furthermore, we discuss the limitations and outline potential research directions for GNNs in disease diagnosis.

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Multi-population phase oscillator networks with higher-order interactions

Cited by 14 publications

References 52 publications

Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks

Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks

Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude

Graph neural networks for image‐guided disease diagnosis: A review

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