Open AccessHOPF BIFURCATION FROM STEADY STATE OF DISSIPATIVE THREE-WAVE INTERACTION
Author(s) -
Kai He
Publication year - 1987
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.36.1451
Subject(s) - hopf bifurcation , eigenvalues and eigenvectors , dissipative system , physics , pitchfork bifurcation , bifurcation , bifurcation theory , transcritical bifurcation , contraction (grammar) , mathematical analysis , classical mechanics , nonlinear system , mathematics , quantum mechanics , medicine
With the analysis of eigenvalues, it is found that a Hopf bifurcation would occur from the steady state of a dissipative three-wave interaction, so long as the contraction rate of its volume in phase space is low enough. The critical value of the contraction rate and the frequencies of the oscillation obtained from the eigenvalues are in good agreement with the results of solving the dynamk equations in the linear stage. It is also shown that no pitchfork bifuraction would occur.