Theory Of Bifurcations Of Dynamic Systems On A Plane

The present monograph is a direct continuation of our Qualitative Theory of Second-Order Dynamic Systems (QT) published in 1966. It may also be considered as a second volume of the definitive treatise on dynamic systems and their applications planned by A. A. Andronov back in the 1940s. All this notwithstanding, however, Theory of Bifurcations can be treated as an independent volume, and the reader is only expected to be acquainted with the basic concepts of the qualitative theory of differential equations on a plane. In distinction from QT, the greater part of which is devoted to the classical theory (of Poincaré and Bendixson), Theory of Bifurcations presents relatively recent results which were obtained during the last three decades and published - in part or completely - in a number of letters and papers in scientific journals. These results are closely linked to the theory of oscillations and have by now found many important uses in physics and engineering.* The present book, like QT, was begun by A. A. Andronov, E. A. Leontovich, and A. G. Maier and completed by E. A. Leontovich and I. I. Gordon. N. A. Gubar' and R. M. Mints also took part in the preparation of the monograph, the former being responsible for Chapter VIII and the latter for part of Chapter XIV. The final version was prepared by I. I. Gordon. The main results presented in Chapters III through VII were derived by A. A. Andronov and L. S. Pontryagin, and those in Chapters IX through XII by A. A. Andronov and E. A. Leontovich. Chapter VIII is based on the work of N. A. Gubar', and the results of Chapter XIII are due to E. A. Leontovich, A. G. Maier, and L. S. Pontryagin. The general editing of the book was undertaken by Yu. M. Romanovskii. The book naturally falls into two parts - the theory of structu