Related papers: The random graph process is globally synchronizing
Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this…
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.…
Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…
Partial, instead of complete, synchronization has been widely observed in various networks including, in particular, brain networks. Motivated by data from human brain functional networks, in this technical note, we analytically show that…
In this work we study the synchronization of Kuramoto oscillators driven by external forces in complex modular networks. The motivation is the neuronal dynamics that takes place during information processing in the neural cortex. The neuron…
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
There are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph Laplacian. Some examples of such models include the Kuramoto and Kuramoto--Sakaguchi…
Generalized synchronization (GS) describes a state in which two coupled dynamical systems exhibit a functional relationship between their variables. GS can be achieved by appropriately designing the coupling to constrain the dynamics onto…
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 synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
We explore synchronization transitions in even-$D$-dimensional generalized Kuramoto oscillators on both complete graphs and $d$-dimensional lattices. In the globally coupled system, analytical expansions of the self-consistency equations,…
Synchronization transition in oscillatory networks manifests itself as the appearance of a periodic global mode. While perfect in the thermodynamic limit, this mode fluctuates for finite ensembles. We characterize the coherence of this mode…
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original,…
Consider any network of $n$ identical Kuramoto oscillators in which each oscillator is coupled bidirectionally with unit strength to at least $\mu (n-1)$ other oscillators. There is a critical value of the connectivity, $\mu_c$, such that…
A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the…
We introduce a novel concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset…
Multi-qubit quantum processors coupled to networking provides the state-of-the-art quantum computing platform. However, each qubit has unique eigenfrequency even though fabricated in the same process. To continue quantum gate operations…
The Kuramoto model (KM) of coupled phase oscillators on graphs provides the most influential framework for studying collective dynamics and synchronization. It exhibits a rich repertoire of dynamical regimes. Since the work of Strogatz and…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…