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Stability Analysis of a System of Exponential Difference Equations

Discrete Dynamics in Nature and Society, 2014
We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn ...
Q. Din, K. A. Khan, A. Nosheen
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Numerical stability for finite difference approximations of Einstein's equations

, 2006
We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol of the second
Alcubierre, Anderson, Arnowitt, Baumgarte, Beyer, Bona, Bona, Calabrese, Calabrese, Frittelli, Frittelli, G. Calabrese, Gundlach, Gundlach, Gustafsson, I. Hinder, Kidder, Knapp, Kreiss, Kreiss, Kreiss, Kreiss, Nagy, Richtmyer, S. Husa, Sarbach, Shibata, Szilágyi, Szilágyi, Teukolsky   +29 more
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Dynamics of a rational system of difference equations in the plane [PDF]

, 2010
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In
Bajo, Ignacio, Franco, Daniel, Perán, Juan   +2 more
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Asymptotic Stability for a Class of Nonlinear Difference Equations

Discrete Dynamics in Nature and Society, 2010
We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a)
Chang-you Wang, Shu Wang, Zhi-wei Wang, Fei Gong, Rui-fang Wang   +4 more
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Bohl-Perron type stability theorems for linear difference equations with infinite delay

, 2010
Relation between two properties of linear difference equations with infinite delay is investigated: (i) exponential stability, (ii) $\l^p$-input $\l^q$-state stability (sometimes is called Perron's property).
Berezansky L., Berezansky L., Daleckiˇ Yu.L., Dunford N., Elaydi S., Elena Braverman, Illya M. Karabash, Liz E., Sasu B.   +8 more
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Birefringent dispersive FDTD subgridding scheme [PDF]

, 2016
A novel 2D finite difference time domain (FDTD) subgridding method is proposed, only subject to the Courant limit of the coarse grid. By making mu or epsilon inside the subgrid dispersive, unconditional stability is induced at the cost of a sparse ...
De Deckere, B, De Zutter, Daniël, Van Londersele, Arne, Vande Ginste, Dries   +3 more
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Stability of a Class of Nonlinear Difference Equations

Journal of Mathematical Analysis and Applications, 1999
Using KAM theory, the authors investigate the stability nature of the zero equilibrium of the system of two nonlinear difference equations \[ \left.\begin{matrix} x_{n+1}=a_1x_n+b_1y_n+f(c_1x_n+c_2y_n)=F_1(x_n,y_n)\\ y_{n+1}=a_2x_n+b_2y_n+f(c_1x_n+c_2y_n)=F_2(x_n,y_n)\end{matrix} \right\}, \quad n=0,1,\dots, \tag{*} \] \(n=0,1,2,\dots\), where \(a_i ...
Papaschinopoulos, G, Schinas, C.J
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Stability of Solutions for a Family of Nonlinear Difference Equations

Advances in Difference Equations, 2008
We consider the family of nonlinear difference equations: xn+1=(∑i=13fi(xn,…,xn−k)+f4(xn,…,xn−k)f5(xn,…,xn−k))/(f1(xn,…,xn−k)f2(xn,…,xn−k)+∑i=35fi(xn,…,xn−k)), n=0,1,…, where ...
Caihong Han, Hongjian Xi, Taixiang Sun
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Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks [PDF]

, 2013
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term ...
Rätz, Andreas, Röger, Matthias
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Hyers–Ulam stability of loxodromic Möbius difference equation [PDF]

Applied Mathematics and Computation, 2019
Hyers-Ulam of the sequence $ \{z_n\}_{n \in \mathbb{N}} $ satisfying the difference equation $ z_{i+1} = g(z_i) $ where $ g(z) = \frac{az + b}{cz + d} $ with complex numbers $ a $, $ b $, $ c $ and $ d $ is defined. Let $ g $ be loxodromic M bius map, that is, $ g $ satisfies that $ ad-bc =1 $ and $a + d \in \mathbb{C} \setminus [-2,2] $.
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