Related papers: Stability and convergence of a higher order ration…
We study the following kth order rational difference equation assuming nonnegative parameters and nonnegative initial conditions $$x_{n}=\frac{\alpha+\sum_{i=1}^{k}\beta_{i}x_{n-i}} {A+\sum_{j=1}^{k}B_{j}x_{n-j}},\quad n\in\mathbb{N}.$$ We…
Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system $\mathbf{x}^{\prime}=P(t)\nabla f(x)$ which arise as critical points of $f$, under the assumption that $P(t)$ is positive semi-definite.…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We consider the linear equation including two fractional order difference operators, viz. $\Delta^{\alpha}$ and $\Delta^{\beta}$, $0<\beta<\alpha \leq 1$. The sequence representation will be provided to find the solution in an easier way.…
In this paper, a proof of asymptotic stability for the combined system-optimizer dynamics associated with a class of real-time methods for equality constrained nonlinear model predictive control is presented. General Q-linearly convergent…
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…
In the present study we highlight some results related to the oscillation for high order nonlinear generalized neutral difference equation in the following form \begin{equation*}…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that…
The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…
Our main goal is to understand the stability of second order linear homogeneous differential equations $\ddot x(t)+\alpha(t)\dot x(t)+\beta(t)x(t)=0$ for $C^0$-generic values of the variable parameters $\alpha(t)$ and $\beta(t)$. For that…
We consider the linear stabilities of the regular n-gon relative equilibria of the (1+n)-body problem. It is shown that there exist at most two kinds of infinitesimal bodies arranged alternatively at the vertices of a regular n-gon when n…
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that…
We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays $$ (x(t)-a(t)x(g(t)))'=-b(t)x(h(t)), $$ where $|a(t)|<1$, $b(t)\geq 0$, $h(t)\leq t$, $g(t)\leq t$, in…
In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows from consistency and stability estimates for the numerical…
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…
We establish the best (minimum) constant for Ulam stability of first-order linear $h$-difference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation…