一类非线性金融系统数学模型的混沌控制
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摘要
研究一类非线性金融系统数学模型的混沌控制.首先,运用动力学方法研究位移反馈控制、加速反馈控制、增强反馈控制、延迟反馈控制在该系统的应用条件和反馈增益系数.其次,运用数值模拟的方法验证各种控制方法的可行性,比较各种控制方法的应用效果.最后选择较好的控制方法,为金融危机的宏观调控提供建议.
This paper study the chaos control for a class of finance systems model. Using the dynamic analysis, the application conditions and the feedback coefficients are studied for the dislocated feedback control method, the speeds feedback control method, the enhancing feedback control method and the delayed feedback control method. Then, using the numerical simulation, the feasibility of the control methods is examined, the control effects of those control method are compared. Finally, the best control method is chosen, and the suggestion for financial crisis macro-control is given.
This paper study the chaos control for a class of finance systems model. Using the dynamic analysis, the application conditions and the feedback coefficients are studied for the dislocated feedback control method, the speeds feedback control method, the enhancing feedback control method and the delayed feedback control method. Then, using the numerical simulation, the feasibility of the control methods is examined, the control effects of those control method are compared. Finally, the best control method is chosen, and the suggestion for financial crisis macro-control is given.
引文
[1] Gao Q, Ma J. Chaos and Hopf bifurcation of a finance system[J]. Nonlinear Dynamic, 2009, 58:209-216.
[2] Chian A C L, Rempel E L, Rogers C. Complex economic dynamics:Chaotic saddle, crisis andintermittency. Chaos Solitons Fractals, 2006, 29(5):1194-1218.
[3] Fanti L, Manfredi P. Chaotic business cycles and fiscal policy:An IS-LM model with distributed tax collection lags. Chaos Solitons Fractals, 2007, 32(2):736-744.
[4]黄登仕,李后强.非线性经济学的理论和方法[M].成都:四川大学出版社,1993.
[5]马军海,陈予恕.一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究(I)[J].应用数学与力学,2001, 22(11):1119-1128.
[6]马军海,陈予恕.一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究(II)[J].应用数学与力学,2001, 22(12):1236-1242.
[7]简国明.金融系统数学模型的机理分析和控制[J].数学的实践与认识,2011, 41(5):1-6.
[8]张学兵.一个新混沌系统的分析和控制[J].重庆师范大学学报(自然科学版),2012, 29(2):55-59.
[9]丁娟,姚洪兴.加速反馈和延迟反馈控制的一个新的混沌系统[J].合肥工业大学学报(自然科学版),2005,28(8):956-960.
[10]陈燕燕.一类金融混沌系统的线性控制模[J].经济数学,2017, 34(4):48-52.
[11]张锦炎,冯贝叶.常微分方程几何理论与分支问题[M].北京:北京大学出版社,2000.
[12]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001.
[2] Chian A C L, Rempel E L, Rogers C. Complex economic dynamics:Chaotic saddle, crisis andintermittency. Chaos Solitons Fractals, 2006, 29(5):1194-1218.
[3] Fanti L, Manfredi P. Chaotic business cycles and fiscal policy:An IS-LM model with distributed tax collection lags. Chaos Solitons Fractals, 2007, 32(2):736-744.
[4]黄登仕,李后强.非线性经济学的理论和方法[M].成都:四川大学出版社,1993.
[5]马军海,陈予恕.一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究(I)[J].应用数学与力学,2001, 22(11):1119-1128.
[6]马军海,陈予恕.一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究(II)[J].应用数学与力学,2001, 22(12):1236-1242.
[7]简国明.金融系统数学模型的机理分析和控制[J].数学的实践与认识,2011, 41(5):1-6.
[8]张学兵.一个新混沌系统的分析和控制[J].重庆师范大学学报(自然科学版),2012, 29(2):55-59.
[9]丁娟,姚洪兴.加速反馈和延迟反馈控制的一个新的混沌系统[J].合肥工业大学学报(自然科学版),2005,28(8):956-960.
[10]陈燕燕.一类金融混沌系统的线性控制模[J].经济数学,2017, 34(4):48-52.
[11]张锦炎,冯贝叶.常微分方程几何理论与分支问题[M].北京:北京大学出版社,2000.
[12]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001.