Hopf Bifurcation within Thermodynamic Representation

Details Hopf Bifurcation within Thermodynamic Representation Hopf Bifurcation within Thermodynamic Representation

2006-04-05

arxiv.org/abs/cond-mat/0604128v2

Physics

Condensed Matter

Statistical Mechanics

9 pages, 1 figure

Scientific paper

On base of Hamiltonian formalism, we show that Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by limit cycle. A revolving phase plane with a set of limit cycles is presented in analogy with revolving vessel containing superfluid He$^4$. Within such a representation, fast varying angle is shown to be reduced to phase of complex order parameter whose module squared plays a role of action. Respectively, vector potential of conjugate field is reduced to relative velocity of movement of the limit cycle interior with respect to its exterior.

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