摘要
本文提出了一种确定二维含参映射系统分叉曲线的数值计算方法,根据最弱的分叉定义(Branching),我们建立了确定周期k解分叉曲线的方程,并给出了方程求解过程中一些基本量的递推关系式,利用本方法编制的计算程序适用于所有的两阶连续可微的二维含参映射系统。作为实例,我们具体计算了Hénon映射和耦合Logistic映射,得到了一些新的结果。
A numerical method has been proposed to calculate the bifurcation curves of parametrized two-dimensional maps. Under the weakest definition of bifurcation (branching.), this method is a direct extension of the idea suggested by one of the authors to general two-dimensional parametrized maps. The recursion formulas required in the calculation have been given. Moreover, the structure of k-period solution on both sides of the bifurcation carves been been discussed from the viewpoint of stability. According to some further definitions of bifurcation, we suggested, a way to determine the bifurcation curves under respective criteria numerically. Two examples of the Henon map and a coupled logistic map have beea treated and some new results'have been obtained.
出处
《力学学报》
EI
CSCD
北大核心
1989年第5期567-574,共8页
Chinese Journal of Theoretical and Applied Mechanics
关键词
含参映射
分叉曲线
打靶法
parameterized map, periodic solution, bifurcation curve, shooting method.
