Stability Analysis of DDEs
This chapter provides some definitions and results on the contractivity, boundedness, and asymptotic stability of test equations chosen from suitable classes of DDEs and neutral DDEs, which are useful for deriving numerical methods that preserve the same properties. Two main possible approaches are reported. One approach (stability for all delays or delay independent stability) involves finding conditions on the right-hand-side function such that the problem is stable for all or some classes of delays, typically for all constant delays. The other approach (stability for fixed delay or delay dependent stability) involves finding weaker conditions such that the desired stability property is guaranteed for specific delay.
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