摘要
文章研究了一类具有非线性分支的分段映射的动力学行为.该模型可能应用到物理科学、工程和医学方面,也有助于一些经济模型的研究.以μ为分岔参数得到系统的分岔图,发现在系统的不变吸引区间内,周期轨道的每个周期点都有一定的存在范围,这造成分岔结构中出现迭代禁区现象.通过理论推导确定了周期轨道周期点的存在范围和禁区边界,进一步通过禁区边界得到了混沌区域与周期n轨道区域的边界的表达式,应用Lyapunov指数对分析结果进行了验证.
In this paper the dynamical behaviors of a class of discontinuous one-dimensional mappings with a nonlinear branch are studied. This kind of models can be used in physical science, engineering, and medical science, and is also help- ful to the study of economics models. Taking/x as a bifurcation parameter to draw the bifurcation diagram of the system, we find that in the invariaut attracting region of the system there is an existence range for each point of the periodic orbit, and it leads to iteration forbidden region appearing in the bifurcation structure. By theoretical derivation, the article determines the existence ranges of the periodic orbits and the boundary of the forbidden region, obtains the boundary expression of the chaot- ic region and the period-n orbits region by the boundary of the forbidden region, and finally verifies the analytic results by the Lyapunov exponents.
作者
许宏飞
李群宏
宁敏
商梦媛
XU Hongfei LI Qunhong NING Min SHANG Mengyuan(School of Mathematics and Information Sciences, Guangxi University, Nanning 530004, Chin)
出处
《海南师范大学学报（自然科学版）》
CAS
2016年第4期363-368,383,共7页
Journal of Hainan Normal University（Natural Science）
基金
广西自然科学基金(2013GXNSFAA019017
2014GXNSFBA118024)
