Dynamics on higher-order networks: A review
Network science has evolved into an indispensable platform for studying complex systems.
But recent research has identified limits of classical networks, where links connect pairs of …
But recent research has identified limits of classical networks, where links connect pairs of …
Intralayer and interlayer synchronization in multiplex network with higher-order interactions
Recent developments in complex systems have witnessed that many real-world scenarios,
successfully represented as networks, are not always restricted to binary interactions but …
successfully represented as networks, are not always restricted to binary interactions but …
The impact of higher-order interactions on the synchronization of Hindmarsh–Rose neuron maps under different coupling functions
In network analysis, links depict the connections between each pair of network nodes.
However, such pairwise connections fail to consider the interactions among more agents …
However, such pairwise connections fail to consider the interactions among more agents …
Cluster synchronization on hypergraphs
A Salova, RM D'Souza - arxiv preprint arxiv:2101.05464, 2021 - arxiv.org
Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with
the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster …
the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster …
Higher-order network interactions through phase reduction for oscillators with phase-dependent amplitude
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 …
If the coupling is weak, phase reduction—the reduction of the dynamics onto an invariant …
[HTML][HTML] Stability analysis of multiplayer games on adaptive simplicial complexes
D Schlager, K Clauß, C Kuehn - Chaos: An Interdisciplinary Journal of …, 2022 - pubs.aip.org
We analyze the influence of multiplayer interactions and network adaptation on the stability
of equilibrium points in evolutionary games. We consider the Snowdrift game on simplicial …
of equilibrium points in evolutionary games. We consider the Snowdrift game on simplicial …
Probability graphons: the right convergence point of view
G Zucal - arxiv preprint arxiv:2407.05998, 2024 - arxiv.org
We extend the theory of probability graphons, continuum representations of edge-decorated
graphs arising in graph limits theory, to the'right convergence'point of view. First of all, we …
graphs arising in graph limits theory, to the'right convergence'point of view. First of all, we …
Random walks and Laplacians on hypergraphs: When do they match?
We develop a general theory of random walks on hypergraphs which includes, as special
cases, the different models that are found in literature. In particular, we introduce and …
cases, the different models that are found in literature. In particular, we introduce and …
Analyzing states beyond full synchronization on hypergraphs requires methods beyond projected networks
A Salova, RM D'Souza - arxiv preprint arxiv:2107.13712, 2021 - arxiv.org
A common approach for analyzing hypergraphs is to consider the projected adjacency or
Laplacian matrices for each order of interactions (eg, dyadic, triadic, etc.). However, this …
Laplacian matrices for each order of interactions (eg, dyadic, triadic, etc.). However, this …
Action convergence of general hypergraphs and tensors
G Zucal - arxiv preprint arxiv:2308.00226, 2023 - arxiv.org
Action convergence provides a limit theory for linear bounded operators $ A_n:
L^{\infty}(\Omega_n)\longrightarrow L^ 1 (\Omega_n) $ where $\Omega_n $ are potentially …
L^{\infty}(\Omega_n)\longrightarrow L^ 1 (\Omega_n) $ where $\Omega_n $ are potentially …