Theory and Applications of Hopf Bifurcation (London Mathematical Society Lecture Note Series, Series Number 41)

This text will be of value to all those interested in and studying the subject in the mathematical, natural and engineering sciences. The `Hopf Bifurcation' describes a phenomenon that occurs widely in the birth of a family of oscillations as a controlling parameter is varied. In a control system consisting of an engine with a centrifugal governor, for example, when the amount of damping associated with the governor is decreased, oscillations can arise, which may significantly disturb normal operation of the engine. Similar oscillations occur in a vast range of animal populations sometimes begin to fluctuate as environmental conditions change, aircraft wing panels begin to flutter in a wind-tunnel as the flow velocity is increased, and nerve tissue initiates production of repeated action potentials as a current stimulus is increased, etc. The phenomena can be described by modelling in terms of systems of ordinary, delay or partial differential equations. The `Hopf Bifurcation' describes a phenomenon that occurs widely in nature: the birth of a family of oscillations as a controlling parameter is varied. In a control system consisting of an engine with a centrifugal governor, for example, when the amount of damping associated with the governor is decreased, oscillations can arise, which may significantly disturb normal operation of the engine. B.d. Hassard, N.d. Kazarinoff And Y.-h. Wan. One Microfiche In Pocket Provides Set Of Computer Programs. Includes Index. Bibliography: P. 300-309.