耗散三波相互作用定态的Hopf分岔

本文讨论了耗散的三波相互作用的一个模型。用本征值分析证明了当相空间体积收缩得足够慢时,三波相互作用的定态将出现Hopf分岔。从本征值得到的定态失稳的临界值和振荡频率,与解运动方程的数字实验在线性阶段符合得很好。分析结果还表明,将不会发生pitchfork分岔。关键词：

HOPF BIFURCATION FROM STEADY STATE OF DISSIPATIVE THREE-WAVE INTERACTION

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.