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- W1974996382 abstract "Through the efforts of many authors, analytic solutions and explicit stability criteria have been developed for many types of linear differentialdelay equations. The treatise of Bellman and Cooke [3] provides a good account of work done before 1963; active research in the field continues up to the present. Besides the concrete results obtained for specific classes of equations, there are also some rough “general principles” that have long guided users of differential-delay equations in their efforts to understand the effects of the various kinds of time delays on stability. One such principle says that instability will be present when the ratio of the time delay to the relaxation time of the system is large. However, the “stability switching” phenomenon, discovered as early as 1948 by Ansoff and Krumhansl [2], contradicts this principle, and a great variety of responses to the presence of time lags are now known. In their landmark paper on the subject, Cooke and Grossman [4] included a series of key examples illustrating the things that can happen. It seems unlikely that any simple general principles will be found to serve as reliable indicators of stability. Instead, we can reasonably hope that the development of further principles of restricted applicability will gradually fill in more of the overall picture. To this end, we introduce a new framework for the classification and representation of differential-delay equations (or “DDE?‘) based on the simplest notions of probability theory. Distributed time delays are represented as probability measures whose expectations and variances can be used to construct intrinsic parameters for the classes of DDEs studied. Intrinsic parametrization has two advantages." @default.
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- W1974996382 date "1992-01-01" @default.
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- W1974996382 title "Intrinsic parameters and stability of differential-delay equations" @default.
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- W1974996382 doi "https://doi.org/10.1016/0022-247x(92)90287-n" @default.
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