二维正弦离散映射的分岔和吸引子

Translated title of the contribution: Bifurcation and attractor of two-dimensional sinusoidal discrete map

毕闯, 张千, 向勇*, 王京梅

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

8 Citations (Scopus)

Abstract

由一个正弦映射和一个三次方映射通过非线性耦合,构成一个新的二维正弦离散映射. 基于此二维正弦离散映射得到系统的不动点以及相应的特征值,分析了系统的稳定性,研究了系统的复杂非线性动力学行为及其吸引子的演变过程。研究结果表明:此二维正弦离散映射中存在复杂的对称性破缺分岔、Hopf分岔、倍周期分岔和周期振荡快慢效应等非线性物理现象。进一步根据控制变量变化时系统的分岔图、Lyapunov指数图和相轨迹图分析了系统的分岔模式共存、快慢周期振荡及其吸引子的演变过程,通过数值仿真验证了理论分析的正确性。

A new two-dimensional sinusoidal discrete map is achieved by nonlinearly coupling a sinusoidal map and with a cubic map. The fixed points and the corresponding eigenvalues are obtained based on this two-dimensional sinusoidal discrete map, and the stability of the system is analyzed to study the complex nonlinear dynamic behavior of the system and the evolutions of their attractors. The research results indicate that there are complex nonlinear physical phenomena in this two-dimensional sinusoidal discrete map, such as symmetry breaking bifurcation, Hopf bifurcation, period doubling bifurcation, periodic oscillation fast-slow effect, etc. Furthermore, bifurcation mode coexisting, fast-slow periodic oscillations and the evolutions of the attractors of the system are analyzed by using the bifurcation diagram, the Lyapunov exponent diagram and the phase portraits when the control parameters of the system are varied, and the correctness of the theoretical analysis is verified based on numerical simulations.

Translated title of the contributionBifurcation and attractor of two-dimensional sinusoidal discrete map
Original languageChinese (Simplified)
Article number240503
Pages (from-to)1-8
Number of pages8
Journal物理学报
Volume62
Issue number24
DOIs
Publication statusPublished - 5 Dec 2013
Externally publishedYes

Keywords

  • 正弦离散映射
  • 对称性破缺分岔
  • Hopf分岔
  • 吸引子
  • sinusoidal discrete map
  • symmetry breaking bifurcation
  • Hopf bifurcation
  • attractor

Fingerprint

Dive into the research topics of 'Bifurcation and attractor of two-dimensional sinusoidal discrete map'. Together they form a unique fingerprint.

Cite this