Related papers: Dynamics controlled by additive noise

Dynamic facilitation theory assumes short-ranged dynamic constraints to be the essential feature of supercooled liquids and draws much of its conclusions from the study of kinetically constrained models. While deceptively simple, these…

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…

The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a…

Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…

In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we…

The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Such asymptotic regime occurs when the system starts from…

Weak noise smooths out fractals in a chaotic state space and introduces a maximum attainable resolution to its structure. The balance of noise and deterministic stretching/contraction in each neighborhood introduces local invariants of the…

Control of underactuated dynamical systems has been studied for decades in robotics, and is now emerging in other fields such as neuroscience. Most of the advances have been in model based control theory, which has limitations when the…

We use a very simple description of human driving behavior to simulate traffic. The regime of maximum vehicle flow in a closed system shows near-critical behavior, and as a result a sharp decrease of the predictability of travel time. Since…

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales.…

We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…

We study the effect of extrinsic noise in metabolic networks. We introduce external random fluctuations at the kinetic level, and show how these lead to a stochastic generalization of standard Metabolic Control Analysis. While Summation and…

This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…

We present a simple dynamical model to address the question of introducing a stochastic nature in a time variable. This model includes noise in the time variable but not in the "space" variable, which is opposite to the normal description…

Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…

This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…

This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…

Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a ``bottom-up'' principle: individuals reorient to maximise their future path entropy over…