Related papers: Foundations of ghost stability
Proceeded from the gravitation equations proposed by one of authors it was argued in a previous paper that there can exist supermassive compact configurations of degenerated Fermi-gas without events horizon. In the present paper we consider…
I report on a systematic derivation of the phenomenological ``adhesion approximation'' from gravitational instability together with a brief evaluation of the related status of analytical modeling of large-scale structure.
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
We study a damped scalar conservation law driven by the sum of a fixed external force and a localised one-dimensional control. The problem is considered in a bounded domain and is supplemented with the Dirichlet boundary condition. It is…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
In this talk I will introduce the principle of stochastic stability and discussing its consequences both at equilibrium and off-equilibrium.
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
This paper establishes absolute stability conditions for nonlinear negative imaginary (NI) systems interconnected with static nonlinear feedback. We first show that the NI property is preserved when the feedback nonlinearity can be…
This article is a contribution to the proceedings of the 33rd/35th International Colloquium on Group Theoretical Methods in Physics (ICGTMP, Group33/35) held in Cotonou, Benin, July 15-19, 2024. The stability of matter is an old and…
We study the general properties of attractors in a cosmological model with tachyonic potential and a scalar field non-minimally coupled to matter. A general analytic formulation is given to derive fixed points with a discussion on their…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
It is not yet known if the global attractor of the space periodic 2D Navier-Stokes equations contains nonstationary solutions $u(x,t)$ such that their energy and enstrophy per unit mass are constant for every $t \in (-\infty, \infty)$. The…
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…
Models with extra dimensions have changed our understanding of the hierarchy problem. In general, these models explain the weakness of gravity by diluting gravity in a large bulk volume, or by localizing the graviton away from the standard…
Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…