物理学报Issue(24)：240503-1-240503-8,8.DOI:10.7498/aps.62.240503
二维正弦离散映射的分岔和吸引子
Bifurcation and attractor of two-dimensional sinusoidal discrete map
摘要
Abstract
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.关键词
正弦离散映射/对称性破缺分岔/Hopf分岔/吸引子Key words
sinusoidal discrete map/symmetry breaking bifurcation/Hopf bifurcation/attractor引用本文复制引用
毕闯,张千,向勇,王京梅..二维正弦离散映射的分岔和吸引子[J].物理学报,2013,(24):240503-1-240503-8,8.基金项目
电子薄膜与集成器件国家重点实验室基础研究开放创新基金(批准号:CXJJ2010001)资助的课题.@@@@Project supported by the Open Innovation Fund for Basic Research of State Key Laboratory of Electronic Thin Films and Integrated Devices, China (Grant No. CXJJ2010001) （批准号:CXJJ2010001）
