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We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
We propose that the size of an operator evolved under holographic renormalization group flow shall grow linearly with the scale and interpret this behavior as a manifestation of the saturation of the chaos bound. To test this conjecture, we…
Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronisation. In this article we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We…
We investigate macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of…
Synchronization underlies phenomena including memory and perception in the brain, coordinated motion of animal flocks, and stability of the power grid. These synchronization phenomena are often modeled through networks of phase-coupled…
Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…
We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…
The high-order synchronization was studied in systems driven by external force and in autonomous systems with proper frequency mismatch. Differing from the literature, in this article, we demonstrate the occurrence of high-order (1:2)…
In this paper, we investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks and modular networks. By adopting the auxiliary-system…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We propose an axiomatic approach for design and performance analysis of noisy linear consensus networks by introducing a notion of systemic performance measure. This class of measures are spectral functions of Laplacian eigenvalues of the…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
The success of contrastive learning is well known to be dependent on data augmentation. Although the degree of data augmentations has been well controlled by utilizing pre-defined techniques in some domains like vision, time-series data…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a…
We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to…
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…
We analyze a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling motivated by the physics of arrays of nanoscale oscillators. We study the model for the mean field case of…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…