Related papers: Lectures on Structural Stability in Dynamics
We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several…
Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
Cosmological singularity and asymptotic behaviour of scale factor of generalized cosmological models are analyzed in respect of their structural stability. It is shown, that cosmological singularity is structurally unstable for the majority…
A discrete--dynamics model, which is specified solely in terms of the system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Recent observational constraints restrict the strict applicability of stellar dynamics in spirals to a few rotation periods. However, stellar dynamics concepts such as periodic orbits are invaluable for understanding the various dynamical…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…