摘要
金融系统是一个由众多要素组成的、开放的、远离平衡态的、极其复杂的非线性系统.在这个非线性系统中,随着各种参数的变化,系统的运动状态由于失稳而出现混沌状态是相当普遍的现象.因此,金融系统的同步发展是众多经济学家面临的一个实际问题.本论文对混沌同步控制问题进行了简要的介绍,在现有同步控制基础上,做了如下一些创新工作：
(1)在一类金融混沌系统的基础上,通过对这类经济模型的分析研究发现,此类经济模型不能真实、准确的反映经济规律的变化,为了更好的反映经济规律的变化,从而提出了一类改进的金融混沌系统.针对这一类改进的金融混沌系统,提出了一种以部分状态变量作为发射信号的混沌系统全局指数同步方法.该方法将驱动系统和响应系统的误差系统分成不同的两个部分.应用微分方程的稳定性理论,分析了系统由局部指数稳定达到整体指数同步需要的条件,并通过数值仿真验证了此方法的有效性；然后提出了一种基于全局指数吸引集的混沌同步方法,引入全局指数吸引集的定义,针对本文所提出的一类改进的混沌金融系统,对其双时滞的混沌同步进行了研究,数值仿真验证了此方法的有效性.
(2)以Routh-Hurwitz判据和Lyapunov稳定性为理论基础,针对一类改进的金融混沌系统,通过设计有效地控制器,对其在参数确定、参数不确定情况下的函数投影同步进行了研究.在参数确定的情况下,利用矩阵方程提出了一种混合反馈控制同步方法、一种基于特殊矩阵结构的反馈控制同步方法；在参数不确定的情况下,利用矩阵方程提出了一种能动反馈控制同步方法.这几种方法的创新之处在于不必去构造繁杂的李雅普诺夫函数,而是将驱动系统与响应系统的同步控制问题转化为误差系统在原点的渐近稳定性问题.论文首先在理论上分析这种方法的可行性,再通过数值试验进行仿真分析,所有结果均证明了几种方法的有效性.
Financial system is an open and complicated nonliear system consisting of many elements, far away from equilibrium points. In this kind of complicated nonliear system, chaotic state appearing with the change of different parameters is a common phenomenon, due to the unbalanced condition of the system. Hence, financial synchronization is a parctical issue that econormists will confront. In this paper, we give a concise description on synchronization of chaotic systems and get the following new results:
(1)Firstly, put forward a kind of modified chaotic finance system based on a kind of chaotic finance system.Then put forward a globally exponentially synchronization method for the kind of modified chaotic finance system with partial state variables as transmission signal. This method is combined with stability theory of differential equation theory, it turns the error system between driving-system and respone-system into two different parts, theory analysis shows the necessary condition of this globally exponentially synchronization method, numerical simulations show the effectiveness of this method. Then we put forward a synchronization method based on globally exponentially attractive set, pull in the definition of globally exponentially attractive set, applying this method to the kind of modified chaotic finance system and numerical simulations show the effectiveness of this method.
(2)Based on Lyapunov stable theory and Routh-Hurwitz critrion theory, some effective controllers are designed for the global asymptotic synchronization on different conditions. This paper investigates the function projective synchronization of the kind of modified chaotic finance systems. When the system parameters are known, the hybrid feedback control and a method based on special matrix structure are adopted respectively to realize the synchronization of the chaotic finance system. When the system parameters are unknown, the active control is extended and introduced to realize the synchronization. Numerical simulations show the validity and the feasibility of the synchronization schemes. The results show that papers from a theoretical analysis of the feasibility of this approach, and then test by numerical simulation results show that this method is simple and design facilitate, results show the validity and the feasibility of the synchronization schemes.
引文
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