一类非对称分数阶经济系统混沌特性及其控制  

Chaotic dynamics in a incommensurate fractional- order nonlinear economic system and its control

作　　者：徐争辉[1] 刘友金[1] 谭文[2] 

机构地区：[1]湖南科技大学商学院 [2]湖南科技大学信息学院,湖南湘潭411201

出　　处：《湖南科技大学学报（社会科学版）》2015年第6期86-91,共6页Journal of Hunan University of Science and Technology(Social Science Edition)

基　　金：国家社科基金重大招标项目(09&ZD041);国家自然科学基金项目(41271139);教育部人文社会科学研究项目(09YJA630032);教育部人文社会科学研究青年项目(10YJC790343);湖南省自然科学基金项目(08JJ3138;14JJ7053);湖南省哲学社会科学项目(09YBB159;湖南省高校科技创新团队资助项目"全球化背景下产业集群竞争力与风险控制研究"

摘　　要：近年来,分数阶系统的动力学行为越来越受到人们的关注。数值仿真显示该系统具有不动点、周期运动和混沌运动等丰富的复杂行为方式。非对称经济系统在阶次小于3时出现混沌现象,由李雅谱若夫指数证实产生混沌的最低阶次仅为2.35,而且也找到了系统从倍周期分叉通往混沌的道路。利用分数阶系统稳定性理论,设计线性反馈控制器,成功地实现了非对称分数阶经济系统所有状态向量与期望目标轨道的跟踪控制,实验结果证实了所设计方法的有效性和可行性。The dynamics of fractional - order system has attracted increasing attention in recent years. The system displays rich dynamical behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in incommensurate fractional - order nonlinear economic system with order less than 3, and the lowest order for this system to yield chaos is 2.35. The results are validated by the exist- ence of positive Lyapunov exponent. A period - doubling routes to chaos in the fractional - order economic system are also obtained. Furthermore, based on the stability theory of fractional - order system , a linear feed- back controller is designed to direct all states of the fractional - order economic system to track desired objective trajactories. The simulation results are presented to demonstrate the effectiveness and feasibility of the proposed method.

关 键 词：混沌动态性 分数微分 非对称分数阶经济系统 线性反馈控制 混沌控制 

分 类 号：F069[经济管理—政治经济学] F224