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Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response of such a network as a function of the prestrain, we consider…

We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in…

Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to…

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…

The most profound effect of disorder on the elastic response of solids is the nonaffinity of local displacements whereby the atoms (particles, network junctions) do not simply follow the macroscopic strain, as they do in perfect crystals,…

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a…

Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on…

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…

The synchronization of power generators is an important condition for the proper functioning of a power system, in which the fluctuations in frequency and the phase angle differences between the generators are sufficiently small when…

Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In…

We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different…

Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph…

Driven by the explosion of data and the impact of real-world networks, a wide array of mathematical models have been proposed to understand the structure and evolution of such systems, especially in the temporal context. Recent advances in…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

When programming network functions, changes within a packet tend to have consequences---side effects which must be accounted for by network programmers or administrators via arbitrary logic and an innate understanding of dependencies.…

In order to model volatile real-world network behavior, we analyze phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects…

We analyze the final state sensitivity of nonlocal networks with respect to initial conditions of their units. By changing the initial conditions of a single network unit, we perturb an initially synchronized state. Depending on the…

Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…

Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…

We discuss the role of monotonicity in enabling numerically tractable modular control design for networked nonlinear systems. We first show that the variational systems of monotone systems can be embedded into positive systems. Utilizing…