Relevant bibliographies by topics / Stability and asymptotics of difference equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Stability and asymptotics of difference equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Stability and asymptotics of difference equations"

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Stević, Stevo. "Global stability and asymptotics of some classes of rational difference equations." Journal of Mathematical Analysis and Applications 316, no. 1 (2006): 60–68. http://dx.doi.org/10.1016/j.jmaa.2005.04.077.

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Kovácsvölgyi, I. "The asymptotic stability of difference equations." Applied Mathematics Letters 13, no. 1 (2000): 1–6. http://dx.doi.org/10.1016/s0893-9659(99)00136-6.

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Medina, Rigoberto. "Stability and asymptotic behavior of difference equations." Journal of Computational and Applied Mathematics 80, no. 1 (1997): 17–30. http://dx.doi.org/10.1016/s0377-0427(96)00151-3.

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Peng, Yuehui. "Global asymptotic stability for nonlinear difference equations." Applied Mathematics and Computation 182, no. 1 (2006): 67–72. http://dx.doi.org/10.1016/j.amc.2006.03.035.

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Wu, Guo–Cheng, and Dumitru Baleanu. "Stability analysis of impulsive fractional difference equations." Fractional Calculus and Applied Analysis 21, no. 2 (2018): 354–75. http://dx.doi.org/10.1515/fca-2018-0021.

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AbstractWe revisit motivation of the fractional difference equations and some recent applications to image encryption. Then stability of impulsive fractional difference equations is investigated in this paper. The fractional sum equation is considered and impulsive effects are introduced into discrete fractional calculus. A class of impulsive fractional difference equations are proposed. A discrete comparison principle is given and asymptotic stability of nonlinear fractional difference equation are discussed. Finally, an impulsive Mittag–Leffler stability is defined. The numerical result is provided to support the analysis.
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Ardjouni, Abdelouaheb, and Ahcene Djoudi. "Asymptotic stability in totally nonlinear neutral difference equations." Proyecciones (Antofagasta) 34, no. 3 (2015): 255–76. http://dx.doi.org/10.4067/s0716-09172015000300005.

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Li, Xianyi, and Deming Zhu. "Global asymptotic stability for two recursive difference equations." Applied Mathematics and Computation 150, no. 2 (2004): 481–92. http://dx.doi.org/10.1016/s0096-3003(03)00286-8.

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Tian, Chuanjun, and Jihong Zhang. "Exponential asymptotic stability of delay partial difference equations." Computers & Mathematics with Applications 47, no. 2-3 (2004): 345–52. http://dx.doi.org/10.1016/s0898-1221(04)90029-6.

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Chen, Fulai, and Zhigang Liu. "Asymptotic Stability Results for Nonlinear Fractional Difference Equations." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/879657.

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We present some results for the asymptotic stability of solutions for nonlinear fractional difference equations involvingRiemann-Liouville-likedifference operator. The results are obtained by using Krasnoselskii's fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results.
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Chan, D. M., E. R. Chang, M. Dehghan, C. M. Kent, R. Mazrooei-Sebdani, and H. Sedaghat. "Asymptotic stability for difference equations with decreasing arguments." Journal of Difference Equations and Applications 12, no. 2 (2006): 109–23. http://dx.doi.org/10.1080/10236190500438357.

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Dissertations / Theses on the topic "Stability and asymptotics of difference equations"

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Jánský, Jiří. "Delay Difference Equations and Their Applications." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233892.

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Disertační práce se zabývá vyšetřováním kvalitativních vlastností diferenčních rovnic se zpožděním, které vznikly diskretizací příslušných diferenciálních rovnic se zpožděním pomocí tzv. $\Theta$-metody. Cílem je analyzovat asymptotické vlastnosti numerického řešení těchto rovnic a formulovat jeho horní odhady. Studována je rovněž stabilita vybraných numerických diskretizací. Práce obsahuje také srovnání s dosud známými výsledky a několik příkladů ilustrujících hlavní dosažené výsledky.
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Kisela, Tomáš. "Basics of Qualitative Theory of Linear Fractional Difference Equations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-234025.

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Tato doktorská práce se zabývá zlomkovým kalkulem na diskrétních množinách, přesněji v rámci takzvaného (q,h)-kalkulu a jeho speciálního případu h-kalkulu. Nejprve jsou položeny základy teorie lineárních zlomkových diferenčních rovnic v (q,h)-kalkulu. Jsou diskutovány některé jejich základní vlastnosti, jako např. existence, jednoznačnost a struktura řešení, a je zavedena diskrétní analogie Mittag-Lefflerovy funkce jako vlastní funkce operátoru zlomkové diference. Dále je v rámci h-kalkulu provedena kvalitativní analýza skalární a vektorové testovací zlomkové diferenční rovnice. Výsledky analýzy stability a asymptotických vlastností umožňují vymezit souvislosti s jinými matematickými disciplínami, např. spojitým zlomkovým kalkulem, Volterrovými diferenčními rovnicemi a numerickou analýzou. Nakonec je nastíněno možné rozšíření zlomkového kalkulu na obecnější časové škály.
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Dvořáková, Stanislava. "The Qualitative and Numerical Analysis of Nonlinear Delay Differential Equations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2011. http://www.nusl.cz/ntk/nusl-233952.

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Disertační práce formuluje asymptotické odhady řešení tzv. sublineárních a superlineárních diferenciálních rovnic se zpožděním. V těchto odhadech vystupuje řešení pomocných funkcionálních rovnic a nerovností. Dále práce pojednává o kvalitativních vlastnostech diferenčních rovnic se zpožděním, které vznikly diskretizací studovaných diferenciálních rovnic. Pozornost je věnována souvislostem asympotického chování řešení rovnic ve spojitém a diskrétním tvaru, a to v obecném i v konkrétních případech. Studována je rovněž stabilita numerické diskretizace vycházející z $\theta$-metody. Práce obsahuje několik příkladů ilustrujících dosažené výsledky.
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Clinger, Richard A. "Stability Analysis of Systems of Difference Equations." VCU Scholars Compass, 2007. http://hdl.handle.net/10156/1318.

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Smith, Dale T. "Expotential decay of resolvents of banded matrices and asymptotics of solutions of linear difference equations." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29218.

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Bonomo, Wescley. "Sistemas dinâmicos discretos: estabilidade, comportamento assintótico e sincronização." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01072008-164134/.

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Este trabalho é em parte baseado no livro The Stability and Control of Discrete Processes de Joseph P. LaSalle. Nós estudamos equações como x(n+1) = T(x(n)), onde T : \' R POT. m\' \' SETA\' \'R POT. m\' é uma aplicação contínua, com o sistema dinâmico associado \'PI\' (n,x) := \' T POT. n\' (x). Nós fornecemos condições suficientes para a estabilidade de equilíbrios usando o método direto de Liapunov. Também consideramos sistemas discretos da forma x(n+1)=T(n, x(n),\'lâmbda\' ) dependendo de uma parâmetro \' lâmbda\' e apresentamos resultados obtendo estimativas de atratores. Finalmente, nós apresentamos algumas simulações de sistemas acoplados como uma aplicação em sistemas de comunicação<br>This work is in part based on the book The Stability and Control of Discrete Processes of Joseph P. LaSalle. We studing equations as x(n+1) = T(x(n)), where T : \' R POT.m\' \' ARROW\' \' \' R POT.m\' is continuous transformation, with the associated dynamic system \'PI\' (n,x) := \' T POT.n\' (x). We provide suddicient conditions for stability of equilibria, using Liapunov direct method. We also consider nonautonomous discrete systems of the form x(n + 1) = T(n, x(n), \' lâmbda\') depending on the parameter \'lâmbda\' and present results obtaining uniform estimatives of attractors. We finally we present some simulations on synchronization of coupled systems as an application on communication systems
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Luís, Rafael Domingos Garanito. "Nonautonomous difference equations with applications." Doctoral thesis, Universidade da Madeira, 2011. http://hdl.handle.net/10400.13/206.

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This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.<br>Henrique Oliveira and Saber Elaydi
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Liu, Xing. "Rigorous exponential asymptotics for a nonlinear third order difference equation." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1101927781.

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Thesis (Ph. D.)--Ohio State University, 2004.<br>Title from first page of PDF file. Document formatted into pages; contains viii, 140 p.; also includes graphics. Includes bibliographical references (p. 139-140).
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Er, Aynur. "Stability of Linear Difference Systems in Discrete and Fractional Calculus." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1946.

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The main purpose of this thesis is to define the stability of a system of linear difference equations of the form, ∇y(t) = Ay(t), and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem. This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are discussed by using particular example. In the second chapter, we focus on solving the linear difference equations by using the undetermined coefficient method and the variation of constants formula. Moreover, we establish the matrix exponential function which is the solution of the initial value problems (IVP) by the Putzer algorithm.
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Göransson, Albin. "Stability and accuracy for difference methods using asynchronous processors." Thesis, Linköpings universitet, Matematiska institutionen, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-146045.

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We solve initial boundary value problems with information unavailable at random time-steps. The randomly unavailable information represents asynchrony between processing elements. To approximate the initial boundary value problem, finite difference operators with summation-by-parts proper-ties and weak boundary procedures are used. Utilizing the energy method, we derive energy estimates for synchronous and asynchronous problems. The simulations show that the solutions may remain accurate and stable, even in the asynchronous case.
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Books on the topic "Stability and asymptotics of difference equations"

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Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1990.

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Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. National Aeronautics and Space Administration, 1990.

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1956-, Dos̆lá Zuzana, and Graef John R. 1942-, eds. The nonlinear limit-point/limit-circle problem. Birkhäuser, 2003.

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Difference equations in normed spaces: Stability and oscillations. Elsevier, 2007.

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Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6.

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Shaĭkhet, L. E. Lyapunov functionals and stability of stochastic difference equations. Springer, 2011.

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P, Matus P., and Vabishchevich P. N, eds. Difference schemes with operator factors. Kluwer Academic, 2002.

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Jeltsch, Rolf. Barriers to the accuracy of explicit three-time-level difference schemes for hyperbolic equations. Universiteit van Stellenbosch, 1992.

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Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer International Publishing, 2013.

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Capietto, Anna. Stability and Bifurcation Theory for Non-Autonomous Differential Equations: Cetraro, Italy 2011, Editors: Russell Johnson, Maria Patrizia Pera. Springer Berlin Heidelberg, 2013.

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Book chapters on the topic "Stability and asymptotics of difference equations"

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Tomášek, Petr. "Asymptotic Stability Regions for Certain Two Parametric Full-Term Linear Difference Equation." In Differential and Difference Equations with Applications. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32857-7_30.

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de Oliveira, Silvia Rodrigues, Soumyendu Raha, and Debnath Pal. "Global Asymptotic Stability of a Non-linear Population Model of Diabetes Mellitus." In Differential and Difference Equations with Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75647-9_29.

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Ivanov, Anatoli F. "Global Asymptotic Stability in a Non-autonomous Difference Equation." In Difference Equations and Discrete Dynamical Systems with Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35502-9_10.

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Izuta, Guido. "Asymptotic Stability of Partial Difference Equations Systems with Singular Matrix." In Lecture Notes in Electrical Engineering. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75605-9_31.

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Lantsman, M. H. "Linear Difference Equations. General Theory." In Asymptotics of Linear Differential Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9797-5_14.

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Sedaghat, Hassan. "Chaos and Stability in Some Models." In Nonlinear Difference Equations. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0417-5_5.

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Elaydi, Saber N. "Stability Theory." In An Introduction to Difference Equations. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-9168-6_4.

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Elaydi, Saber N. "Stability Theory." In An Introduction to Difference Equations. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-3110-1_4.

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Lantsman, M. H. "Asymptotic Behaviour of Solutions of Linear Difference Equations." In Asymptotics of Linear Differential Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9797-5_15.

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Shaikhet, Leonid. "Difference Equations as Difference Analogues of Differential Equations." In Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6_10.

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Conference papers on the topic "Stability and asymptotics of difference equations"

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Nguyen-Van, Triet, and Noriyuki Hori. "A Discrete-Time Model for Lotka-Volterra Equations With Preserved Stability of Equilibria." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63049.

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A Lotka-Volterra differential equation is discretized using a method proposed recently by the same authors for nonlinear autonomous systems and the stability of equilibrium points of the resulting discrete-time model is investigated. It is shown that when Jacobian matrix of the nonlinear equation is invertible, the equilibrium points of the model are identical to those of the original continuous-time system, and their asymptotic stability and instability are retained for any sampling period. While the method can be applied to any Lotka-Volterra types, simulation results are presented for a competitive-type example, where the continuous-time system and their discrete-time models obtained by the forward-difference, Mickens’, Kahan’s, and the proposed methods are compared. They illustrate that, in general, the proposed model performs better than other discrete-time models.
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Elaydi, Saber. "Recent Developments in the Asymptotics of Difference Equations." In Proceedings of the Third International Conference on Difference Equations. CRC Press, 2017. http://dx.doi.org/10.4324/9780203745854-11.

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Fedotov, A., and F. Klopp. "Difference equations, uniform quasiclassical asymptotics and Airy functions." In 2018 Days on Diffraction (DD). IEEE, 2018. http://dx.doi.org/10.1109/dd.2018.8553493.

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Bas, Erdal, and Ramazan Ozarslan. "Asymptotics of eigenfunctions for Sturm-Liouville problem in difference equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952075.

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Cheng, Sui. "Stability of Partial Difference Equations." In Proceedings of the Third International Conference on Difference Equations. CRC Press, 2017. http://dx.doi.org/10.4324/9780203745854-9.

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Řehák, Petr. "A note on asymptotics and nonoscillation of linear $q$-difference equations." In The 9'th Colloquium on the Qualitative Theory of Differential Equations. Bolyai Institute, SZTE, 2012. http://dx.doi.org/10.14232/ejqtde.2012.3.12.

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Li, Hongfei, and Lijun Zhang. "Stability of Difference-Integral Delay Equations." In 2020 39th Chinese Control Conference (CCC). IEEE, 2020. http://dx.doi.org/10.23919/ccc50068.2020.9188694.

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KAMONT, Z. "STABILITY OF DIFFERENCE - FUNCTIONAL EQUATIONS AND APPLICATIONS." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0004.

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Kolmanovskii, V. B., J. F. Lafay, and J. P. Richard. "Riccati equations in stability theory of difference equations with memory." In 1999 European Control Conference (ECC). IEEE, 1999. http://dx.doi.org/10.23919/ecc.1999.7099894.

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Zhang, Shunian. "Estimate Of Stability Region For Delay Difference Equations." In Proceedings of the Third International Conference on Difference Equations. CRC Press, 2017. http://dx.doi.org/10.4324/9780203745854-26.

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Reports on the topic "Stability and asymptotics of difference equations"

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Holmes, Mark Alan. Stability of finite difference approximations of two fluid, two phase flow equations. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/505672.

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Cloutman, L. D. A note on the stability and accuracy of finite difference approximations to differential equations. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/420369.

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