【摘要】 文中对一维映象引入函数通过证明在倍周期分岔点上进一步解析地证明了在倍周期分岔点上本文讨论了在数字计算中函数[G的操作行为,分析表明在μ趋近分岔点时反常增大,在给定的前置迭代次数下,其最大值所对应的μ_n是分岔点μ_n的下限,因而为识别临界慢化与分岔提供了判据。根据上述结果,文中建议了一个利用数字计算确定分岔点位值的方法并给出一个计算实例。更多还原

【Abstract】 In this paper we introduce a function G（2² ,μ,x）≡（/μ）F（2ⁿ,μ,x） and prove that G（2ⁿ,μ,x）=0 at the period-doubling bifurcation points, we discuss also the operation behavior of the function [G（2ⁿ,μ,x）^-1]. Analysis shows that the function [G（2ⁿ,μ, x）]^-1 will be increacing anomalously as μ go to bifurcation points μ_n.When N. the number of the prepositive iterating operation time is given, the μ_n corresponding to the maximum ,of [G（2ⁿ,x）]^-1is a lower limit of the bifurcation point μ_n.Conse-quently, we provide here a criterion to distingush between the critical low down and the bifurcation.In addition we suggest a method to determine the locations of bifurcation points using numerical computation, according to the results above, and an example are also presented.更多还原