Abstract
The role of the comparison method, as already studied in Section II.3, might be roughly characterized as follows: the solutions of the comparison equation push on before themselves those of the original equation. Following V. M. Matrosov [1973], this can be viewed as an interesting extension of the notion of a mathematical model. In the usual sense, a mathematical model operates approximately like the system it represents, whereas the solutions of the comparison equation fit approximately those of the original one, but while remaining “on the same side” at any time. One might speak of a one-sided model. The comparison method is sufficiently important in itself to justify the presence here of a complete chapter devoted to this subject. Further, it introduces to some typical applications.
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© 1977 Springer-Verlag, New York Inc.
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Rouche, N., Habets, P., Laloy, M. (1977). The Comparison Method. In: Stability Theory by Liapunov’s Direct Method. Applied Mathematical Sciences, vol 22. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9362-7_9
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DOI: https://doi.org/10.1007/978-1-4684-9362-7_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90258-6
Online ISBN: 978-1-4684-9362-7
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