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It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network…
Spreading information through a network of devices is a core activity for most distributed systems. As such, self-stabilizing algorithms implementing information spreading are one of the key building blocks enabling aggregate computing to…
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…
In recent years, tremendous progress has been made in understanding the dynamics of vehicle traffic flow and traffic congestion by interpreting traffic as a multi-particle system. This helps to explain the onset and persistence of many…
This paper gives a fresh look at network synchronization. Here we no longer analyze it from the view of mathematics, such as graph theory, while we probe into one from control theory. First, we analyze the synchronization region using the…
The robustness of connectivity and the efficiency of paths are incompatible in many real networks. We propose a self-organization mechanism for incrementally generating onion-like networks with positive degree-degree correlations whose…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We…
During the past few decades wireless technology has seen a tremendous growth. The recent introduction of high-end mobile devices has further increased subscriber's demand for high bandwidth. Current cellular systems require manual…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
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…
This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize…
Self-organized systems, from synthetic nanostructures to developing organisms, are composed of fluctuating units capable of forming robust functional structures despite noise. Here, we ask: are there fundamental bounds on the robustness of…
Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the…
A self-organization of efficient and robust networks is important for a future design of communication or transportation systems, however both characteristics are incompatible in many real networks. Recently, it has been found that the…
We propose a variation of the self organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
Biological systems often consist of a small number of constituents and are therefore inherently noisy. To function effectively, these systems must employ mechanisms to constrain the accumulation of noise. Such mechanisms have been…