Nonlinear Dynamics

, Volume 70, Issue 4, pp 2313–2326

Complexity analysis research of financial and economic system under the condition of three parameters’ change circumstances

Original Paper


This paper studies the characteristics of a series of complex systems, which are in combination of interest rate, investment, and price index parameters meeting the condition cbabc≥0, including stable node, saddle points, bifurcation, Hopf bifurcation, and chaos, and the corresponding mathematical expressions of Lyapunov index are given. Based on this, we perform complexity analysis of the system and study the change circumstances of Lyapunov index when one or two parameters synchronously change. Numerical simulation results verify the theoretical analysis and conclusion. The results of this economic and financial system provide reference to practical problems, and have a positive effect on the actual application of the system of this type.


Nonlinear economic system Saddle point Hopf bifurcation Lyapunov exponent impression Complex dynamics 


  1. 1.
    Huang, D., Li, H.: The Theory and Method of Nonlinear Economics, pp. 55–60. Sichuan University Press, ChengDu (1993) Google Scholar
  2. 2.
    Moez, F.: An adaptive chaos synchronization scheme applied to secure communications. Chaos Solitons Fractals 18(1), 141–148 (2003) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Ding, J., Yao, W.: Chaos control of a kind of non-linear finance system. J. Jiangsu Univ. 15(6), 500–504 (2004) MathSciNetGoogle Scholar
  4. 4.
    Song, Y.: Chaos control of a kind of non-linear finance system. D. Huazhong Univ. Sci. Technol. (2006) Google Scholar
  5. 5.
    Freedman, H.I., Singh, M., Easton, A.K., Baggs, I.: Mathematical models of population distribution within a culture group. Math. Comput. Model. 29(6), 257–267 (1999) MathSciNetGoogle Scholar
  6. 6.
    Chian, A.C.L., Borotto, F.A., Rempel, E.L.: Attractor merging crisis in chaotic business cycles. Chaos Solitons Fractals 25(5), 869–875 (2005) CrossRefGoogle Scholar
  7. 7.
    Gao, S., Chen, L.: Dynamic complexities in a single-species discrete population model with stage structure and birth pulses. Chaos Solitons Fractals 23(1), 519–527 (2005) MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Ma, J., Gao, Q.: Analysis on the chaotic motion of a stochastic nonlinear dynamic system. Int. J. Comput. Math. 87(14), 3266–3272 (2010) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Xin, B., Ma, J.: Neimark–Sacker bifurcation in a discrete-time financial system. Discrete Dyn. Nat. Soc. 2010, 405639 Google Scholar
  10. 10.
    Gao, Q., Ma, J.: Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn. 58, 209–216 (2009) MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Szydlowski, M., Krawiec, A.: The stability problem in the Kaldor–Kalecki business cycle model. Chaos Solitons Fractals 25(7), 299–305 (2005) MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Cai, G.: Synchronization analysis for a kind of modified chaotic finance systems. D. Jiangsu Univ. (2010) Google Scholar
  13. 13.
    Ma, J., Zhang, Q., Gao, Q.: Stability of a three-species symbiosis model with delays. Nonlinear Dyn. 67, 567–572 (2012) MATHCrossRefGoogle Scholar
  14. 14.
    Sun, Z., Ma, J.: Complexity of triopoly price game in Chinese cold rolled steel market. Nonlinear Dyn. 67(3), 2001–2008 (2012) CrossRefGoogle Scholar
  15. 15.
    Xu, C., Liao, M., He, X.: Stability and bifurcation analysis in a delayed Lotka–Volterra predator–prey model with two delays. Int. J. Appl. Math. Comput. Sci. 21(1), 97–107 (2011) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.College of Management and EconomicsTianjin UniversityTianjinChina
  2. 2.Tianjin University of Finance and EconomicsTianjinChina

Personalised recommendations