相关论文: On the stability of solutions of certain linear se…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a…
In this paper, we provide a system-theoretic treatment of certain continuous-time homogeneous polynomial dynamical systems (HPDS) via tensor algebra. In particular, if a system of homogeneous polynomial differential equations can be…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.
We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
The method and the formula of variation of constants for ordinary differential equations (ODEs) is a fundamental tool to analyze the dynamics of an ODE near an equilibrium. It is natural to expect that such a formula works for delay…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…
In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…
The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An…
PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval. However, solutions to these PDEs often do not converge to a…
Eigenvalue perturbation theory is applied to justify using complex-valued linear scalar test equations to characterize the stability of implicit-explicit general linear methods (IMEX GLMs) solving autonomous linear ordinary differential…
This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas.…
In this work, we primarily focus on the two-phase solutions and their stability to the focusing mKdV equation. By employing the algebro-geometric approach in combination with an effective integration method, we construct explicit two-phase…
The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.