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Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
The ability to detect weak distributed activation patterns in networks is critical to several applications, such as identifying the onset of anomalous activity or incipient congestion in the Internet, or faint traces of a biochemical spread…
We have investigated the role that different connectivity regimes play on the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random connectivity…
We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First,…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
In networked systems, stochastic resonance occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external…
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 study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
Network structure or connectivity pattern is critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure,…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
The complexity of modern control systems necessitates architectures that achieve high performance while ensuring robust stability, particularly for nonlinear systems. In this work, we tackle the challenge of designing output-feedback…
Various functions of a network of excitable units can be enhanced if the network is in the `critical regime', where excitations are, on average, neither damped nor amplified. An important question is how can such networks self-organize to…