具有重叠结构的非线性吸引予的维数估计

利用质量分布原理,给出了不满足任何分离条件从而具有重叠结构的非线性吸引子的Hausdorff维数下界的一个估计,也就是:设J为R中非空紧子集,Si(x)in=1为一簇二次可微的压缩映射,且满足以下条件:1)对任意i∈I,Si(J)J,2)对任意i∈I,x∈J,0<a≤|Si′(x)|≤b<1。K为J在迭代函数系统Si(x)in=1下的非线性吸引子,假如∩i∈ImSi(K)=,则dimHK≥sm,这里sm>0且满足maxA∈Ωm∑i∈A(Si′)dm-sm=1,Ωm为所有m级最大重叠序列的集合,dm满足∑i∈Im(S′i)dm=1,且Si′=minx∈J{Si′(x)}。

Homogenization of attractors for a class of nonlinear parabolic equations

The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.

锁模光纤激光器的偏振同步与去同步动力学

基于正色散的非线性偏振旋转(NPR)锁模光纤激光器,在稳定的连续波(CW)锁模状态和复合锁模状态下分析脉冲的偏振特性。通过单一调节泵浦功率,实现稳定的CW锁模状态下耗散孤子(DS)与类噪声(NLP)两种脉冲的切换。另外,固定泵浦功率,仅调节偏振控制器(PCs)可得到由脉冲状态自发切换引起的复合锁模状态。对比分析两种锁模状态下的脉冲偏振特性,发现纵模相位锁定的同步对应于脉冲正交偏振分量的完全同步,纵模相位在同步与去同步切换状态下的复合锁模对应于脉冲正交偏振分量的部分同步。实验结果表明,纵模相位间的同步状态受脉冲正交偏振分量影响。该工作对理解锁模激光器中复杂动力学、发展稳定的激光动力学技术具有指导意义。

A Tentative Nonlinear Model for Explanation of a Perceptual Alternation Phenomenon

We present a simple three-neuron Hopfield neural network as a tentative model to illustrate the perspective alternation of Necker cube. This neural network has a chaotic attractor with two "leaves", each leaf can be regarded as a dynamic process corresponding a feature of the Necker cube. This tentative model suggests another manifestation of the role of chaos in information processing.