Open AccessBifurcation and attractor of two-dimensional sinusoidal discrete map
Author(s) -
Chen Bi,
Qian Zhang,
Yong Xiang,
Wang Jing-Mei
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.240503
Subject(s) - bifurcation diagram , phase portrait , attractor , bifurcation , period doubling bifurcation , lyapunov exponent , saddle node bifurcation , mathematical analysis , physics , nonlinear system , oscillation (cell signaling) , mathematics , quantum mechanics , biology , genetics
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.