一类生产函数混沌性质的讨论

Analysis on Chaos Nature of a Production Function

讨论参数 μ、λ变化对动力系统xn + 1=μxn(1-xλn)的影响。通过计算机模拟得出如下结果 :此动力系统的性质以其轨道的聚点个数为标志 ,当某一参数取定某一值 ,另一参数值在不同范围 ,聚点数不同 ,即动力系统处于不同状态 ;从一状态变到另一状态 ,其过渡过程产生混沌 ;聚点个数与参数取值关系的图象是一个分形结构。

The paper discusses and influence on dynamical system X n+1 =μX n(1-X λ n) owing to the change of parameters μ and λ .Computer simulation found that the nature of this dynamical system has been characterized by the number of its trace accumulation points.When one parameter is defined,the other changes in different ranges,and the number of accumulation point changes at the same time.i.e.the system get different state.When system state changes,its transitional process results in Chaos.The diagram of parameter quantity and accumulation points shown a fractal structure. [WT5HZ]