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Avtomatika i Telemekhanika, 2011, Issue 9, Pages 87–98
(Mi at2276)
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This article is cited in 5 scientific papers (total in 5 papers)
Topical issue
Maximum periodic solutions of the Volterra integrodifferential equations in the critical case of a pair of pure imaginary roots
V. S. Sergeev Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia
Abstract:
Systems with aftereffect are considered, which are described by integrodifferential equations of the Volterra type in the presence of a small perturbation prescribed by the periodic (or maximum periodic) time function. In the critical case of a pair of pure imaginary roots of a characteristic equation, the question is solved as to existence in the system of maximum periodic motions (i.e., motions tending at the unlimited increase of time to periodic modes) provided that the frequency of the periodic part of disturbance coincides with the natural frequency of a linearized homogeneous system. It is shown that in the analytic case the equations of motion of the system possess a set of the maximum periodic solutions representable by power series in a small parameter specifying a value of the disturbance, and in small arbitrary initial values of uncritical variables of the problem. The conditions of the existence of such solutions are indicated, which are defined by the terms up to the third order of equations.
Citation:
V. S. Sergeev, “Maximum periodic solutions of the Volterra integrodifferential equations in the critical case of a pair of pure imaginary roots”, Avtomat. i Telemekh., 2011, no. 9, 87–98; Autom. Remote Control, 72:9 (2011), 1876–1886
Linking options:
https://www.mathnet.ru/eng/at2276 https://www.mathnet.ru/eng/at/y2011/i9/p87
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Abstract page: | 190 | Full-text PDF : | 45 | References: | 29 | First page: | 6 |
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