Geodesic
The theory of nonclassical relaxation oscillations in singularly perturbed delay systems
Sbornik. Mathematics, Tome 205 (2014) no. 6, pp. 781-842

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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 $y(t-h)$, $h=\mathrm{const}>0$, and with a small parameter $\varepsilon>0$ 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 $\varepsilon\to 0$ and the $y$-component is shaped like a $\delta$-function, are investigated. The results obtained are illustrated by several examples from ecology and laser theory. Bibliography: 11 titles.
Keywords: nonclassical relaxation oscillations, singularly perturbed delay systems, asymptotic behaviour, stability. 
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. The theory of nonclassical relaxation oscillations in singularly perturbed delay systems. Sbornik. Mathematics, Tome 205 (2014) no. 6, pp. 781-842. http://geodesic.mathdoc.fr/item/SM_2014_205_6_a2/