Related papers: Designing precise dynamical steady states in disor…
We investigate the stability problem for discrete-time stochastic switched linear systems under the specific scenarios where information about the switching patterns and the probability of switches are not available. Our analysis focuses on…
While modern deep networks have demonstrated remarkable versatility, their training dynamics remain poorly understood--often driven more by empirical tweaks than architectural insight. This paper investigates how internal structural choices…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…
We briefly introduce the generic framework of Disordered Elastic Systems (DES), giving a short `recipe' of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of…
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…
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…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…
In many complex systems, the dynamical evolution of the different components can result in adaptation of the connections between them. We consider the problem of how a fully connected network of discrete-state dynamical elements which can…
We provide a rigorous justification of various kinetic regimes exhibited by the nonlinear Schr\"{o}dinger equation with an additive stochastic forcing and a viscous dissipation. The importance of such damped-driven models stems from their…
As networks and their structure have become a major field of research, a strong demand for network visualization has emerged. We address this challenge by formalizing the well established spring layout in terms of dynamic equations. We thus…
In regimes where inertia is negligible, the temporal evolution is governed by overdamped dynamics. This limit is particularly relevant in soft-matter contexts, such as polymers, colloidal suspensions, and processes occurring at the cellular…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
This work aims to propose and design a class of networks of coupled linear and nonlinear oscillators, in which short bursts of exogenous excitation result in sustained endogenous network activity that returns to a quiescent state only after…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
Nature provides examples of self-assemble lightweight disordered network structures with remarkable mechanical properties which are desirable for many applications purposes but challenging to reproduce artificially. Previous experimental…
Disordered soft materials, such as fibrous networks in biological contexts exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…