The monograph deals with singularly perturbed systems of ordinary differential equations and parabolic partial differential equations and continues investigations of the first monograph of E. F. Mishchenko and N. Kh. Rozov [Differential equations with small parameters and relaxation oscillations, Nauka, Moscow, 1975, English translation: Plenum Press, New York and London (1980; Zbl 0482.34004)]. The main results given in the book were obtained by the authors in recent years. The list of references is not complete and includes mainly works of the authors.
Chapter 1 is devoted to the study of the problem of uniqueness and stability for multidimensional relaxation cycles and construction of full asymptotics of relaxation oscillations. Relaxation tori of singularly perturbed systems are considered. Chapter 2 deals with oscillations of a singularly perturbed system of parabolic equations of the reaction-diffusion type. In chpater 3 a normal form of mappings in the neighbourhood of a relaxation cycle is constructed and bifurcations of a relaxation cycle are studied. The following two chapters deal with so-called duck-trajectories of relaxation systems and relaxation cycles of Lotka-Volterra systems. In the last chapter autowave processes in singularly perturbed parabolic systems with small diffusion are studied.