一类经济模型的随机动力学行为分析

发布时间：2018-03-16 11:26

本文选题：经济系统　切入点：Chebyshev正交多项式　出处：《北方民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：在全球经济不断发展的情况下,经济运行受到各种各样复杂因素的影响,经济学中传统的研究方法显得捉襟见肘.非线性经济学的迅速发展,为当前复杂的经济运行状况提供了新的研究思路和方法,并逐渐成为当代经济学的研究趋势.本文运用非线性随机动力学理论中的研究方法,对经济系统中的非线性现象以及复杂的运行规律进行了研究,并对其内部不确定因素的影响进行了分析,主要完成了以下工作:首先,简述了经济系统的国内外发展现状,阐述了当前随机动力学理论的研究现状,介绍了受随机因素影响的非线性动力学系统的理论分析方法、稳定性、动力学行为.其次,应用Chebyshev正交多项式逼近法研究了一类含有界随机参数经济系统的Hopf分岔现象,将随机系统转化成等价的确定性系统,并得到系统发生Hopf分岔的条件,然后通过数值模拟验证了理论结果的正确性.结果表明:受随机因素的影响,系统表现出复杂的非线性特性,并得出参数随机强度?逐渐增大时不仅使系统分岔参数值左移,且会抑制极限环幅值的增大,从而达到控制极限环幅值的目的.再次,研究了一类非线性经济周期模型在谐和随机噪声激励下的内在复杂性.利用Lyapunov直接法研究了系统未扰运动的零解稳定性,得出系统在平衡点是渐近稳定的.采用多尺度法求解出方程的一阶近似解,讨论了激励频率中的小量与其一阶近似解幅值之间的关系,并得出系统参数的变化对响应振幅的影响是十分显著的.最后,总结了论文的主要工作与结论、创新点,给出继续深入研究的方向和建议.
[Abstract]:With the continuous development of the global economy, the economic operation is affected by various complicated factors, and the traditional research methods in economics are overstretched. It provides a new research idea and method for the current complex economic operation, and gradually becomes the research trend of contemporary economics. In this paper, we use the research method of nonlinear stochastic dynamics theory. In this paper, the nonlinear phenomena and complex operating rules in economic system are studied, and the influence of internal uncertainties is analyzed. The main work is as follows: firstly, the development status of economic system at home and abroad is briefly described. In this paper, the current research situation of stochastic dynamics theory is described, and the theoretical analysis method, stability and dynamic behavior of nonlinear dynamical systems affected by random factors are introduced. The Chebyshev orthogonal polynomial approximation method is used to study the Hopf bifurcation of a class of economic systems with bounded stochastic parameters. The stochastic system is transformed into an equivalent deterministic system, and the conditions for the Hopf bifurcation of the system are obtained. Then the correctness of the theoretical results is verified by numerical simulation. The results show that the system exhibits complex nonlinear characteristics and the random strength of the parameters is obtained by the influence of random factors. When increasing gradually, it not only makes the bifurcation parameter value shift to the left, but also inhibits the increase of limit cycle amplitude, thus achieving the purpose of controlling the limit cycle amplitude. In this paper, the inherent complexity of a class of nonlinear business periodic models under harmonic random noise excitation is studied. The stability of zero solution of unperturbed motion of the system is studied by Lyapunov direct method. It is concluded that the system is asymptotically stable at the equilibrium point. The first order approximate solution of the equation is solved by using the multi-scale method, and the relation between the small quantity in the excitation frequency and the amplitude of the first order approximate solution is discussed. Finally, the paper summarizes the main work and conclusions of the paper, innovation points, and gives the direction and suggestions for further research.
【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F113;O211.6

【参考文献】