一个参数未知的网格多涡卷超混沌系统的自适应同步

提出一个网格多涡卷超混沌系统, 该系统在x,y两个方向上扩展鞍焦平衡点, 可产生任意个数的涡卷. 通过Lyapunov指数谱、 平衡点、 分岔图、 复杂度等动力学分析, 系统在较大的参数区间内呈超混沌状态, 且随着涡卷数的增加, 系统的复杂度和最大Lyapunov指数均明显增加, 系统的动力学行为变得更复杂. 根据Lyapunov指数稳定理论,  研究系统参数未知的自适应同步. 数值实验结果表明, 该方法的同步时间较短, 同步效果较好.

A Self adaptive Nonnegative Matrix Factorization Algorithm

Firstly, by introducing adaptive strategy, we proposed a self adaptive nonnegative matrix factorization based on gradient descent. Secondly, bycomparing the distance between reconstructed nonnegative matrix and self adaptive regulation, the problems of randomness and the number of basic vectors validation for traditional nonnegative matrix factorization were solved, and the basic vectorsgenerated by the algorithm were more representative. Finally, taking the analysis and validation of undergraduate achievement ofa college of Jilin University as an example, we investigated effectiveness of the proposed algorithm. The experimental results show that compared with the traditional nonnegative matrix method, the self adaptive nonnegetive matrix factorization method has better robutness and reduces the error rate by 20.16%.