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Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
This Report discusses a recently developed concept of Limiting Phase Trajectories (LPTs) providing a unified description of resonant energy transport in a wide range of classical and quantum dynamical systems with constant and time-varying…
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We study the occurrence of frequency synchronised states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network,…
Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…
Recently, we proposed polycontextural networks as a model of evolving systems of interacting beliefs. Here, we present an analysis of the phase transition as well as the scaling properties. The model contains interacting agents that strive…
A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…