Related papers: The Gentlest Ascent Dynamics
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
The main properties of a dynamical system can be analyzed by examining the corresponding basins, either attraction basins in dissipative systems or escape basins in open Hamiltonian systems and area-preserving maps. In the latter case, the…
Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
In this paper we investigate some properties of equilibrium points in n-dimensional linear control systems with saturated state feedback. We provide an index formula for equilibrium points and discuss its relation to boundaries of…
This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method,…
Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
We provide an explicit method to construct dynamical systems which admit an a-priori prescribed attracting set. As application, we provide a method to construct perturbations of conservative dynamical systems, which admit an a-priori…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…
We study a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical…
In this work, we reveal a strong implicit bias of stochastic gradient descent (SGD) that drives overly expressive networks to much simpler subnetworks, thereby dramatically reducing the number of independent parameters, and improving…
We study the stability of deterministic systems given sequences of large, jump-like perturbations. Our main result is to dervie a lower bound for the probability of the system to remain in the basin, given that perturbations are rare…
Vanishing gradients and overfitting are central problems in machine learning, yet are typically analyzed in asymptotic regimes that obscure their dynamical origins. Here we provide a dynamical description of learning in multi-layer…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Perpetual points (PPs) are special critical points for which the magnitude of acceleration describing dynamics drops to zero, while the motion is still possible (stationary points are excluded), e.g. considering the motion of the particle…
This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…