Related papers: Fibration Symmetries and Cluster Synchronization i…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
We study the homogeneous Kuramoto model on a graph and the geometry of its underlying optimization landscape $\min_{\boldsymbol \theta \in \mathbb R^n}-\sum_{1\leq i,j\leq n} A_{ij}\cos(\theta_i-\theta_j).$ This problem admits a dual…
The problem of partitioning a power grid into a set of microgrids, or islands, is of interest for both the design of future smart grids, and as a last resort to restore power dispatchment in sections of a grid affected by an extreme…
Different models such as diffusion-collision and nucleation-condensation have been used to unravel how secondary and tertiary structures form during protein folding. However, a simple mechanism based on physical principles that provide an…
The collective dynamics in populations of magnetic spin torque oscillators (STO) is an intensely studied topic in modern magnetism. Here, we show that arrays of STO coupled via dipolar fields can be modeled using a variant of the Kuramoto…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…
A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a {\em hill climb} scheme in which the edges of the network are swapped in order…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…
Cluster synchronization underlies various functions in the brain. Abnormal patterns of cluster synchronization are often associated with neurological disorders. Deep brain stimulation (DBS) is a neurosurgical technique used to treat several…
Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology. A fundamental and long-time goal in the study of synchronisation has been to find…
The emergence of synchrony essentially underlies the functionality of many systems across physics, biology and engineering. In all established synchronization phase transitions so far, a stable synchronous state is connected to a stable…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
Synchronization in various complex networks is significantly influenced by higher-order interactions combined with non-Gaussian stochastic perturbations, yet their mechanisms remain mainly unclear. In this paper, we systematically…
A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under…