相关论文: Stability in Distribution of Neutral Stochastic Fu…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative…
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
The properties of stability of compact set $\mathcal{K}$ which is positively invariant for a semiflow $(\Omega\times W^{1,\infty}([-r,0],\mathbb{R}^n),\Pi,\mathbb{R}^+)$ determined by a family of nonautonomous FDEs with state-dependent…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under…
In this paper, we consider the solvability problems for the fully coupled forward-backward stochastic difference equations (FBS{\Delta}Es) on spaces related to discrete time, finite state processes. On one hand, we provide the necessary and…
We develop a mathematical framework for determining the stability of steady states of generic nonlinear reaction-diffusion equations with periodic source terms, in one spatial dimension. We formulate an \textit{a priori} condition for the…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…
In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly…