Theory and Applications of Hopf Bifurcation (London Mathematical Society Lecture Note Series, Series Number 41) – B. D. Hassard Favoriet

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. Similar oscillations occur in a vast range of situations: animal populations sometimes begin to fluctuate as environ…