Related papers: Dynamical systems with a prescribed attracting set…
To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transportation authorities have implemented managed lane policies, which restrict certain freeway lanes to certain types of vehicles. It was…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…
Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
Background: Autocatalytic sets are often considered a necessary (but not sufficient) condition for the origin and early evolution of life. Although the idea of autocatalytic sets was already conceived of many years ago, only recently have…
Investigate the stochastic dynamic non-linear system with the Wiener and the Poisson perturbations. For such systems we construct the program control with probability one, which allows this system to move on the given trajectory. In this…
We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part I deals with driving paths of finite…