厄农映射
厄农映射(英语:Hénon map)是一种可以产生混沌现象的离散时间动态系统,其迭代表达式为:
在经典厄农映射中,参数值分别取为a = 1.4及b = 0.3。此时,系统表现出混沌现象。而当a与b取其他不同值时,系统可表现为混沌现象、阵发性现象,或收敛至周期点。通过轨道图可以看出不同参数下系统的行为特征。
厄农映射是由法国数学家米歇尔·厄农提出的,以此作为洛伦茨模型的庞加莱截面的简化模型。对经典厄农映射而言,任意初始点或趋向厄农奇异吸引子,或发散至无穷大。厄农吸引子具有分形结构,其在一个方向上连续,另一个方向上则为一个康托尔集。数值计算表明经典厄农吸引子的关联维数为1.25 ± 0.02[1],豪斯多夫维数为1.261 ± 0.003。[2]
参考文献
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