含指数项广义平方映射的分岔和吸引子

Bifurcation and attractor of generalized square map with exponential term

由平方映射延伸构造出了一类含指数项的广义平方映射,并由一维映射通过一次耦合项得到了二维映射.利用一参数分岔图、二参数动力学行为分布图、映射迭代曲线和吸引子相图等方法对这类广义平方映射进行了分析和仿真.研究结果表明:一维广义平方映射分布在一个单位区域内的,有着与单峰平方映射相类似的非线性动力学现象;而二维广义平方映射则存在Hopf分岔和锁频等现象,有着复杂多变、形状奇异的极限环和混沌吸引子.

By extending the square map,a one-dimensional generalized square map with exponential term is constructed,and its corresponding two-dimensional map is obtained via one-order coupled item in this paper. By using the one-parameter bifurcation diagram,two-parameter dynamics behavior distribution diagram,iterative mapping curve and attractor phase graphics,these 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 map,and two-dimensional generalized square map has the phenomenon of Hopf bifurcation and locked-frequency shown with complex,flexible and strange-shaped limit cycles and chaotic attractors.