复合Ginzburg-Landau方程的动力学行为分析

目前对非线性波动方程的研究大都仅限于静态波解,即所考虑的波解的波速、振幅、波宽都是不变的,考虑动态波解,以复合Ginzburg-Landau(CGLE)方程为研究对象,探讨其动力学行为.在假设示性函数的基础上,所研究的无穷维耗散系统转化为三维向量场,给出了简单分岔和Hopf分岔存在的条件,揭示了系统平衡点和极限环随系统参数的变化规律,分析了参数平面的不同区域中系统的相图特性,得到系统存在两种不同频率的周期解,此外还数值模拟了系统由倍周期分岔导致混沌的过程,揭示了系统的复杂性.

Dynamical Analysis of the Complex Ginzburg-Landau Equation

The dynamical behavior of the cubic-quintic complex Ginzburg-Landau equation (CGLE) has been investigated in this paper.Based on the assumption of a special trial function,a three-dimensional vector field has been derived from the infinite-dimensional dissipative system.The conditions of two types of possible bifurcation phenomena,i.e., simple bifurcation corresponding to change of the fixed points and Hopf bifurcation associated with limit cycles,have been presented,which may divide the parameter space into regions associated with different phase portraits.Two kinds of periodic solutions with different frequencies have been observed.Furthermore,a cascading of period-doubling bifurcations has been observed,which leads the system to chaos,implying the complexity of the vector field.