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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].

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34K20 Stability theory of functional-differential equations
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