Related papers: Statistical stability of saddle-node arcs
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a…
In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.
We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get that a certain natural two-dimensional extension of the classical one-dimensional…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
The streamwise roll and streak structure (RSS) is prominent in observations of the planetary boundary layer in the atmosphere and ocean and in unstratified wall-bounded shear flows. Although the RSS in these systems is structurally similar,…
Time-periodic perturbations of an asymmetric Duffing-Van-der-Pol equation close to an integrable equation with a homoclinic "figure-eight" of a saddle are considered. The behavior of solutions outside the neighborhood of "figure-eight" is…
The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical…
We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use…
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are…
In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…
Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We…
Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…
The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I…