Related references
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Summary: We investigate the influence of structured higher-order interactions on the collective behavior of coupled phase oscillators. Using a combination of hypergraph generative model and dimensionality reduction techniques, we derive a reduced system of differential equations for the order parameters of the system. By studying a hypergraph with hyperedges of sizes 2 and 3, we obtain a set of two coupled nonlinear algebraic equations for the order parameters. The system exhibits bistability and explosive synchronization transitions under strong coupling via triangles, and we validate our predictions with numerical simulations. Our results provide a general framework to study synchronization of phase oscillators in hypergraphs with various characteristics.
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Per Sebastian Skardal et al.
Summary: We investigate synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We discover that the combination of these two properties leads to several states that cannot be supported by either higher-order interactions or community structure alone, such as synchronized states with communities organized into clusters in-phase, anti-phase, and a novel skew-phase, as well as an incoherent-synchronized state. Additionally, the system exhibits strong multistability, with many of these states simultaneously stable. We validate our findings by deriving the low dimensional dynamics of the system and analyzing its bifurcations using stability analysis and perturbation theory.
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Mathematics, Applied
Xin-Jian Xu et al.
Summary: The threshold model on hypergraphs is studied in this paper, and a theoretical framework based on generating function technology is developed to derive the cascade condition and the giant component of vulnerable vertices. It is found that hyperedges play a dual role in propagation, and the heterogeneity of thresholds, hyperdegrees, and hyperedges affects the fragility and robustness of the system. The higher hyperdegree a vertex has, the larger possibility and faster speed it will get activated.
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M. A. Lohe
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Mathematics, Applied
Fatemeh Parastesh et al.
Summary: This study investigates the higher-order interactions among neurons and finds that second-order interactions can lead to synchronization under lower first-order coupling strengths. Additionally, the introduction of three-body interactions reduces the overall synchronization cost.
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Mathematics, Applied
Cameron Ziegler et al.
Summary: This study uses techniques from algebraic topology to investigate consensus dynamics on edges in simplicial complexes, revealing how higher-order and lower-order interactions influence the balance and convergence speed of dynamics, as well as the effect of network topology on consensus dynamics.
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Dibakar Ghosh et al.
Summary: Complex network theory has provided an ideal framework for studying the relationships between the connectivity patterns and emergent synchronized functioning in systems. This review summarizes the major results of contemporary studies on synchronization in time-varying networks, focusing on two paradigmatic frameworks. It also discusses promising directions and open problems for future research.
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Mathematics, Applied
Nicholas W. Landry et al.
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Mathematics, Applied
Daniela Schlager et al.
Summary: We analyze the influence of multiplayer interactions and network adaptation on the stability of equilibrium points in evolutionary games. Through studying the Snowdrift game on simplicial complexes, we find that rational best-response strategies are difficult to destabilize even with higher-order multiplayer interactions.
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Mathematics, Applied
Md Sayeed Anwar et al.
Summary: Recent developments in complex systems have shown that real-world scenarios can be successfully represented as hypergraphs, allowing for higher-order interactions beyond pairwise interactions. This study investigates the intralayer and interlayer synchronizations of a multiplex hypergraph structure, revealing that the consideration of higher-order interactions significantly enhances intralayer synchronization and that interlayer synchronization is more persistent in multiplex hypergraphs with many-body interactions compared to those with only pairwise interactions.
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Mathematics, Applied
Florian Klimm
Summary: This study focuses on investigating dynamic processes on networks and reveals that contagion processes can provide information about the embedding of nodes in a Euclidean space. The activation times of threshold contagions are used to construct contagion maps as a manifold-learning approach. However, contagion maps are computationally expensive, and thus this study demonstrates that truncating the threshold contagions can significantly speed up the construction of contagion maps. The results show that contagion maps can be used to find insightful low-dimensional embeddings for single-cell RNA-sequencing data and reveal biological manifolds.
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Mathematics, Applied
Abdorasoul Ghasemi et al.
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Mathematics, Applied
Desmond John Higham et al.
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Mathematics, Applied
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Mathematics, Applied
Eddie Nijholt et al.
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Sourin Chatterjee et al.
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Ivan Leon et al.
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