具时滞反馈金融系统的动力学分析与混沌控制  

Dynamic Analysis and Chaos Control of a Finance System with Delayed Feedbacks

作　　者：杨纪华[1] 张二丽[2] 刘媚[1] yang Jihua Zhang Erli Liu Mei(Department of Mathematics and Computer Science, Ningxia Normal University, Ningxia Guyuan 756000 School of Information Engineering, Zhengzhou Institute of Finance and Economics, Zhengzhou 450001)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000 [2]郑州财经学院信息工程学院,郑州450001

出　　处：《数学物理学报（A辑）》2017年第4期767-782,共16页Acta Mathematica Scientia

基　　金：宁夏科技支撑计划项目(KJ[2015]26(4));国家自然科学基金(11361046);宁夏青年科技人才托举工程;河南省高等学校重点科研项目(16A110038);宁夏师范学院重点科研项目(NXSFZD1708)~~

摘　　要：研究了时滞反馈对金融系统的动力学行为的影响.以时滞为分支参数,研究了系统平衡点的局部稳定性,并发现当时滞经过一系列临界值时,系统在平衡点附近经历Hopf分支和Hopf-zero分支.然后,应用规范型方法和中心流形理论得到决定分支周期解性质的详细公式.通过设计合适的反馈增益和时滞,混沌振荡可以控制为稳定的平衡点或周期轨.最后,数值模拟验证了理论结果.We investigate the effect of delayed feedbacks on a finance system. Choosing the delays as the bifurcation parameters, the local stability of the equilibrium is studied and the Hopf bifurcation and Hopf-zero bifurcation happen while the delay passes through a sequence of critical values. For determining the properties of bifurcating periodic solutions, we derive explicit formulae by using the normal form method and the center manifold theory. By designing appropriate feedback strength and delay, chaotic oscillation can be controlled to be a stable equilibrium or stable periodic orbits. Finally, a numerical example is taken to confirm the theoretical results.

关 键 词：稳定性 HOPF分支 Hopf-zero分支 混沌控制 

分 类 号：O175[理学—数学]