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Title: The theory of nonclassical relaxation oscillations in singularly perturbed delay systems

Some special classes of relaxation systems are introduced, with one slow and one fast variable, in which the evolution of the slow component x(t) in time is described by an ordinary differential equation, while the evolution of the fast component y(t) is described by a Volterra-type differential equation with delay y(t−h), h=const>0, and with a small parameter ε>0 multiplying the time derivative. Questions relating to the existence and stability of impulse-type periodic solutions, in which the x-component converges pointwise to a discontinuous function as ε→0 and the y-component is shaped like a δ-function, are investigated. The results obtained are illustrated by several examples from ecology and laser theory. Bibliography: 11 titles. (paper)
Authors:
;  [1] ;  [2]
  1. Yaroslavl' State University (Russian Federation)
  2. Moscow State University (Russian Federation)
Publication Date:
OSTI Identifier:
22365111
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 6; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DELTA FUNCTION; DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS; OSCILLATIONS; PERIODICITY; RELAXATION; STABILITY; VOLTERRA INTEGRAL EQUATIONS