Algebraic approach for the exploration of the onset of chaos in discrete nonlinear dynamical systems

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• 作者：Minvydas Ragulskis^a ; ^{minvydas.ragulskis@ktu.lt} ; ; Zenonas Navickas^b ; ¹ ; ^{zenonas.navickas@ktu.lt} ; Rita Palivonaite^a ; ² ; ^{rita.palivonaite@ktu.lt} ; Mantas Landauskas^a ; ³ ; ^{mantas.landauskas@ktu.lt}
• 关键词：Hankel matrix ; Rank of a sequence ; Algebraic decomposition ; Onset of chaos
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 期刊代码：89_10075704
• 类别：ph
• 出版时间：November, 2012
• 卷：17
• 期：11
• 页码：4304-4315
• 文件大小：1599 K

摘要

An algebraic approach based on the rank of a sequence is proposed for the exploration of the onset of chaos in discrete nonlinear dynamical systems. The rank of the partial solution is identified and a special technique based on Hankel matrices is used to decompose the solution into algebraic primitives comprising roots of the modified characteristic equation. The distribution of roots describes the dynamical complexity of a solution and is used to explore properties of the nonlinear system and the onset of chaos.