Algorithm and Mathematica Realization about Logistic Mapping Bifurcation Point
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- 英文论文题名：Algorithm and Mathematica Realization about Logistic Mapping Bifurcation Point
- 论文作者：HOU Xiang-lin ; WANG Jia-xiang
- 英文论文作者：HOU Xiang-lin ; WANG Jia-xiang ; School of Mechanical Engineering ; Shenyang Jianzhu University ; School of Civil Engineering ; Shenyang Jianzhu University
- 年：2017
- 作者机构：School of Mechanical Engineering,Shenyang Jianzhu University;School of Civil Engineering,Shenyang Jianzhu University;
- 英文论文关键词：algebra mapping ; bifurcation values ; nonlinear equations
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O175
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：4
- 文件大小：407k
- 原文格式：D
- 会议级别：全国
摘要
Algebraic dynamical system and Logistic mapping system was studied in this paper. Through the establishment of nonlinear equations in bifurcation points, the solution of the bifurcation values problem is analyzed. A more precise period-doubling bifurcation point optimization is proposed. Based on Mathematica program process, the optimization results are given. The precise bifurcation values and the corresponding coordinates are obtained. A simple and feasible accurate calculation principle of the bifurcation values is provided for a class of algebraic mapping system.
Algebraic dynamical system and Logistic mapping system was studied in this paper. Through the establishment of nonlinear equations in bifurcation points, the solution of the bifurcation values problem is analyzed. A more precise period-doubling bifurcation point optimization is proposed. Based on Mathematica program process, the optimization results are given. The precise bifurcation values and the corresponding coordinates are obtained. A simple and feasible accurate calculation principle of the bifurcation values is provided for a class of algebraic mapping system.
Algebraic dynamical system and Logistic mapping system was studied in this paper. Through the establishment of nonlinear equations in bifurcation points, the solution of the bifurcation values problem is analyzed. A more precise period-doubling bifurcation point optimization is proposed. Based on Mathematica program process, the optimization results are given. The precise bifurcation values and the corresponding coordinates are obtained. A simple and feasible accurate calculation principle of the bifurcation values is provided for a class of algebraic mapping system.
引文
[1]Li,T.Y.,&Yorke,J.A.(1975).Period three implies chaos.American Mathematical Monthly,82(10),985-992.
[2]Mandelbrot B B.The fractal geometry of nature[M].New York:Plenum Press,1982.25-30.
[3]Chang,G.,&Sederberg,T.W.(1997).Over and over again.DBLP.231-240.
[4]Liao,N.H.,&Gao,J.F.(2006).Chaotic spreading sequences generated by the extended chaotic map and its performance analysis.Journal of Electronics&Information Technology,28(7),1255-1257.
[5]Feigenbaum,M J.Universality Behavior in nonlinear System.Los Alamos Science,1980,14~27
[6]Hao B L.Fractal,chaos,st range at tractors,onflow and others[J].Physics Evolution,1983,3(3):213-242.
[7]Takens,F.(1981).Detecting strange attractors in turbulence.Dynamical Systems and Turbulence,Warwick 1980.Springer Berlin Heidelberg.
[8]LIU Jun,HOU Xiang-lin,WANG Dan-min,WANG Tie-guang,Optimum Algorithm for Bifurcation of Logistic Mapping,Journal of Northeastern University,21(5):580~582,2000.
[9]LI Yong-qiang,LIU Jie,HOU Xiang-lin,Optimum Algorithm for Bifurcation of Algebra Iterated Mapping,Journal of Northeastern University,2003,24(5).
[10]HOU Xiang-lin,HAN Xu,A Fast High-Precision Algorithm for Ramification Value of Nonlinear Algebraic Mapping Problems,Journal of Northeastern University,26(4):344~346,2005.
[2]Mandelbrot B B.The fractal geometry of nature[M].New York:Plenum Press,1982.25-30.
[3]Chang,G.,&Sederberg,T.W.(1997).Over and over again.DBLP.231-240.
[4]Liao,N.H.,&Gao,J.F.(2006).Chaotic spreading sequences generated by the extended chaotic map and its performance analysis.Journal of Electronics&Information Technology,28(7),1255-1257.
[5]Feigenbaum,M J.Universality Behavior in nonlinear System.Los Alamos Science,1980,14~27
[6]Hao B L.Fractal,chaos,st range at tractors,onflow and others[J].Physics Evolution,1983,3(3):213-242.
[7]Takens,F.(1981).Detecting strange attractors in turbulence.Dynamical Systems and Turbulence,Warwick 1980.Springer Berlin Heidelberg.
[8]LIU Jun,HOU Xiang-lin,WANG Dan-min,WANG Tie-guang,Optimum Algorithm for Bifurcation of Logistic Mapping,Journal of Northeastern University,21(5):580~582,2000.
[9]LI Yong-qiang,LIU Jie,HOU Xiang-lin,Optimum Algorithm for Bifurcation of Algebra Iterated Mapping,Journal of Northeastern University,2003,24(5).
[10]HOU Xiang-lin,HAN Xu,A Fast High-Precision Algorithm for Ramification Value of Nonlinear Algebraic Mapping Problems,Journal of Northeastern University,26(4):344~346,2005.