Теорія періодичної множини граничних циклів, що народжуються внаслідок біфукації хопфа

Abstract

On the base of the Hamiltonian formalism, we show that the Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by the limit cycle. A revolving phase plane with a set of limit cycles is presented in analogy with the revolving vessel containing superfluid He 4 . Within such a representation, fast varying angle is shown to be reduced to the phase of complex order parameter whose module squared plays a role of action. Respectively, the vector potential of the conjugate field is reduced to the relative velocity of motion of the limit cycle interior with respect to its exterior. From the physical point of view, it means that nontrivial self-organized system suppresses entirely external periodical fields with frequencies w0 bounded by a limit wc1 within the domain wc1 <w0 <wc2 this field arrives at the resonance series whose coordinates and momenta are varied within the periodically distributed domains. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/1695