Related papers: Generic balanced synchrony patterns in network dyn…

Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…

Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…

We study dynamical transportation networks in a framework that includes extensions of the classical Cell Transmission Model to arbitrary network topologies. The dynamics are modeled as systems of ordinary differential equations describing…

We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as…

We study a network of finitely many interacting clusters where each cluster is a collection of globally coupled circle maps in the thermodynamic (or mean field) limit. The state of each cluster is described by a probability measure, and its…

Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating…

In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on…

Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…

The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network…

The synchronization of human networks is essential for our civilization, and understanding the motivations, behavior, and basic parameters that govern the dynamics of human networks is important in many aspects of our lives. Human ensembles…

Synchronizability of stable, output-coupled, identical, time-varying linear systems is studied. It is shown that if the observability grammian satisfies a persistence of excitation condition, then there exists a bounded, time-varying linear…

The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of systems with one-dimensional internal dynamics and with…

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…

In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable…

The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g…

We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues…

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…

We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…

Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active…

Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to…