Regional Problems in Modern-Day Migration of the Rural Population

Recently, the problem of rural migration has attracted the unflagging attention of scientists and practical workers. This is the result of a certain lag in the study of the problem as well as of the great changes that have taken place in technical development and in the distribution of socialist production. These changes not only intensify general population mobility and occupational mobility in accordance with the requirements of the development of the national economy but also bring about certain disproportions in the distribution of labor resources between city and village, by branch of production, and by area.

Nonlinear phenomena in a high–power heating unit with pulse modulated control

In this paper we describe the transitions from regular periodic mode to quasiperiodicity that can be observed in a pulse–width modulated control system for a high–power heating unit. The behavior of such a system can be described by a set of two coupled nonautonomous differential equations with discontinuous right–hand sides. We reduce the investigation of this system to the studying of a two–dimensional piecewise–smooth map. We demonstrate how a closed invariant curve associated with quasiperiodic dynamics can arise from a stable periodic motion through a Neimark-Sacker bifurcation. The paper also considers a variety of interesting nonlinear phenomena, including phase-locking modes, multistablilty and hysteretic transitions