两个模态耦合的Ginzburg-Landau方程的时空混沌同步化

根据数值计算的结果提出了模态耦合的条件，两个方程在高频模态上是耦合的，而在低频模态上是不耦合的．利用了无穷维动力系统理论，证明了两个高频模态耦合的Ginzburg-Landau方程在函数空间中存在吸引域，因而存在连通的、有限维的紧的整体吸引子．驱动方程存在时空混沌．将方程组联系一个截断形式，得到的修正方程组将保持原方程组的动力学行为．高频模态耦合的两个方程在一定的条件下具有挤压性质，证明了可达到完全的时空混沌同步化．在数学上定性解释了无穷维动力系统的同步化现象．研究方法不同于有限维动力系统中通常使用的Liapunov函数方法与近似线性方法．

Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations

On the basis of numerical computation,the conditions of the modes coupling were proposed.The high-frequency modes are coupled,but the low frequency modes are uncoupled.It was proved that the existence of an absorbing set and a global finite dimensional attractor which is compact,connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE).The trajectory of driver equation may be spatio-temporal chaotic.One associats with MGLE,a truncated form of the equations.The prepared equations will persist in long time dynamical behavior of MGLE.MGLE possess the squeezing properties under some conditions.It was proved that the complete spatio-temporal chaotic synchronization for MGLE can occur.Synchronization phenomenon of infinite dimensional dynamical system(IFDDS)was illustrated on the mathematical theory qualitatively.The method is different from Liapunov function methods and approximate linear methods.