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Stability Analysis of Fractional Difference Equations with Delay [PDF]

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the “fractional order difference,” can also have a long-time memory.
Divya D. Joshi, Sachin Bhalekar, Prashant M. Gade   +2 more
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Global Stability of a Rational Difference Equation [PDF]

Discrete Dynamics in Nature and Society, 2010
We consider the higher‐order nonlinear difference equation xn+1 = (p + qxn−k)/(1 + xn + rxn−k), n = 0, 1, … with the parameters, and the initial conditions x−k, …, x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above‐mentioned equation. In
Tang Guo-Mei, Lin-Xia Hu, Ma Gang
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Advanced Discrete Halanay-Type Inequalities: Stability of Difference Equations

Journal of Inequalities and Applications, 2009
We derive new nonlinear discrete analogue of the continuous Halanay-type inequality. These inequalities can be used as basic tools in the study of the global asymptotic stability of the equilibrium of certain generalized difference equations.
Kim Young-Ho, Agarwal RaviP, Sen SK
doaj   +3 more sources

Stability of generalized Newton difference equations

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012
In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations Δn(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam ...
Wang Zhihua, Shi Yong-Guo
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Stability and Stabilization of Impulsive Stochastic Delay Difference Equations [PDF]

Discrete Dynamics in Nature and Society, 2010
When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable?
Kaining Wu, Xiaohua Ding, Liming Wang
doaj   +4 more sources

Stability of Volterra difference delay equations

Electronic Journal of Qualitative Theory of Differential Equations, 2006
We study the asymptotic stability of the zero solution of the Volterra difference delay equation \begin{equation} x(n+1)=a(n)x(n)+c(n)\Delta x(n-g(n))+\sum^{n-1}_{s=n-g(n)}k(n,s)h(x(s)).\nonumber \end{equation} A Krasnoselskii fixed point theorem is ...
Ernest Yankson
doaj   +3 more sources

Global Asymptotic Stability in a Class of Difference Equations

Advances in Difference Equations, 2008
We study the difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui ...
Jianqiu Cao, Yuan Yan Tang, Limin Cui, Xiaofan Yang   +3 more
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Existence, Uniqueness, and Stability of Solutions for Nabla Fractional Difference Equations [PDF]

Fractal and Fractional
In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties.
Nikolay D. Dimitrov, Jagan Mohan Jonnalagadda   +1 more
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Stability Analysis and Periodictly Properties of a Class of Rational Difference Equations

MANAS: Journal of Engineering, 2022
The goal of this study is to investigate the global, local, and boundedness of the recursive sequenceT_{η+1}=r+((p₁T_{η-l₁})/(T_{η-m₁}))+((q₁T_{η-m₁})/(T_{η-l₁}))+((p₂T_{η-l₂})/(T_{η-m2}))+((q₂T_{η-m₂})/(T_{η-l₂}))+...+((p_{s}T_{η-l_{s}})/(T_{η-m_{s}}))+(
Elsayed Elsayed, Badriah Aloufi
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Global Asymptotic Stability of a Nonautonomous Difference Equation [PDF]

Journal of Applied Mathematics, 2014
We study the following nonautonomous difference equation:xn+1=(xnxn-1+pn)/(xn+xn-1),n=0,1,…, wherepn>0is a period-2 sequence and the initial valuesx-1,x0∈(0,∞). We show that the unique prime period-2 solution of the equation above is globally asymptotically stable.
Gumus, Mehmet, Ocalan, Ozkan
openaire   +6 more sources