Kipnis, M. M.; Levitskaya, I. S. Stability of delay difference and differential equations: similarities and distinctions. (English) Zbl 1127.39017 Elaydi, S. (ed.) et al., Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25–30, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-643-0/hbk). 315-324 (2007). Summary: We compare the stability domains in the space of the parameters for the pair of differential and difference equations \(\dot x(t)=Ax(t-\tau)\) and \(x_n-x_{n-1}=Ax_{n-k}\) in \(\mathbb{R}^m\), as well as the pair of scalar equations with two delays \(\dot x(t)=ax(t-\tau_1)+bx(t-\tau_2)\) and \(x_n-x_{n-1}=ax_{n-m}+bx_{n-k}\).For the entire collection see [Zbl 1117.39001]. Cited in 3 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34K20 Stability theory of functional-differential equations Keywords:asymptotic stability; delay differential equation; stability domains; difference equations PDFBibTeX XMLCite \textit{M. M. Kipnis} and \textit{I. S. Levitskaya}, in: Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25--30, 2005. Hackensack, NJ: World Scientific. 315--324 (2007; Zbl 1127.39017)