Related papers: Nonlinear Diffusion on Networks: Perturbations and…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…
Network-linked data, where multivariate observations are interconnected by a network, are becoming increasingly prevalent in fields such as sociology and biology. These data often exhibit inherent noise and complex relational structures,…
Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered…
In this paper we study a discrete time consensus model on a connected graph with monotonically increasing peer-pressure and noise perturbed outputs masking a hidden state. We assume that each agent maintains a constant hidden state and a…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…
A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…