Open AccessBifurcation and attractor of generalized square map with exponential term
Author(s) -
Bocheng Bao,
Kang Zhu-Sheng,
Jianzhong Xu,
Hu Wen
Publication year - 2009
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.58.1420
Subject(s) - bifurcation diagram , attractor , square (algebra) , bifurcation , unit square , exponential function , mathematics , hopf bifurcation , mathematical analysis , nonlinear system , statistical physics , physics , geometry , quantum mechanics
By extending the square mapa one-dimensional generalized square map with exponential term is constructedand its corresponding two-dimensional map is obtained via one-order coupled item in this paper. By using the one-parameter bifurcation diagramtwo-parameter dynamics behavior distribution diagramiterative mapping curve and attractor phase graphicsthese generalized square maps are analyzed and simulated. The research results indicate that one-dimensional generalized square map distributes in the unit region and has the nonlinear dynamical phenomenon similar to single-peak square mapand two-dimensional generalized square map has the phenomenon of Hopf bifurcation and locked-frequency shown with complexflexible and strange-shaped limit cycles and chaotic attractors.