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Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…

Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type…

The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…

Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The…

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…

Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…

We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…

We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social…

Network cascade refers to diffusion processes in which outcome changes within part of an interconnected population trigger a sequence of changes across the entire network. These cascades are governed by underlying diffusion networks, which…

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced…

Given a reaction-diffusion system interacting via a complex network, we propose two different techniques to modify the network topology while preserving its dynamical behaviour. In the region of parameters where the homogeneous solution…

This paper introduces a diffusion-based planner for leader--follower formation control in cluttered environments. The diffusion policy is used to generate the trajectory of the midpoint of two leaders as a rigid bar in the plane, thereby…

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable,…