基于切延迟的椭圆反射腔的吸引子研究

本文使用转移矩阵的方法，引入椭圆角转换函数，使椭圆问题得到简化，推导出十分简单的切延迟椭圆反射的迭代公式，这样非常有利于理论分析.切延迟椭圆反射腔映射系统(TD-ERCS)在切延迟1单位时存在吸引子，利用该公式，对其吸引子形成的原因及稳定性做了理论分析，发现圆的吸引子与椭圆不尽相同；同时发现椭圆有两个不动线，但只有一个是稳定的.本文还发现，随着椭圆压缩因子μ的减小，对于任意的切延迟因子m，相邻两次迭代数据间的相关性增强，这说明将该系统用作密码系统，椭圆压缩因子μ不能太小，同时混沌系统本身要求μ不能太大，否则降低安全度.关键词：混沌切延迟TD-ERCS吸引子

Study of attractor based on tangent-delay for elliptic reflecting cavity

By introducing the conversion function on ellipse angle, we use the method of shift matrix to achieve the simplification of ellipse problem. A very simple iterative formula is deduced on the tangent-delay for elliptic reflection, which is very useful for theoretical analysis. There exits a chaotic attractor when tangent delays one unit in TD-ERCS. The origin of the attractor and its stability are analyzed in theory. We find that the attractors in the circular and the elliptic cases are not entirely the same; the ellipse has two immobile lines, but only one of them is steady. We also find that, with the decrease of ellipse compression factor μ, the correlation of nearby iterative data is strengthened when the tangent-delay factor m is arbitrary. It means that in using the system for cryptography, the ellipse compression factor μ can not be too small, and the chaos system requires that it should not be too big, otherwise the degree of safety will be reduced.