摘要
根据Frobenius-Perron方程,可以对混沌映射的不变分布从理论上加以分析,从而对混沌映射不变分布作出大致的估计.由此可以利用符号计算的方法求解得到迭代函数系统不变分布的密度近似函数,从而逼近理论解.用几个计算实例和常见数值解法作了比较,试验结果表明符号计算方法具有一定的优势.
Based on the analysis of Probenius-Perron equation,the invariant probability distribution of a chaotic mapping can be studied theoretically and it is possible to estimate it. However,by using symbolic computation method,it is easy to get a series of functions that approximate to the theoretical invariant probability distribution.It has been shown that the symbolic computation method has its particular advantage compared with other numerical computation methods by applying them to several examples.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第6期171-177,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(60802026)
国家重点基础研究发展计划(2006CB910700)
暨南大学青年基金(51208030)
关键词
迭代函数系统
不变分布
数值计算
符号计算
iterated-function systems
invariant probability distribution
numerical computation
symbolic computation
