Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (5): 835-844.doi: 10.3969/j.issn.1005-3085.2022.05.012

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Dynamic Evolution Analysis of the New Financial Duffing-Holms Model and Its Control

ZHAO Yue1,   XU Yuhua1,   XIE Chengrong2   

  1. 1. School of Finance, Nanjing Audit University, Nanjing 211815
    2. School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815
  • Online:2022-10-15 Published:2022-12-15
  • Contact: Y. Xu. E-mail address: yuhuaxu2004@163.com
  • Supported by:
    The National Natural Science Foundation of China (62176127; 61673221); the Six Talent Peaks Project in Jiangsu Province (DZXX-019); the Major Natural Science Foundation of Jiangsu Higher Education Institutions (20KJA120002); the Open Project of Jiangsu Financial Engineering Laboratory (NSK2021-09); the Applied Economics Advantage Subject Construction Project of Jiangsu Higher Education Institutions ([2018]87); the Postgraduate Training Innovation Program of Jiangsu Province (KYCX21-1856).

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Abstract:

In this paper, a new financial Duffing-Holms chaotic model is proposed, and the basic dynamical properties of the system are discussed, such as Hopf bifurcation, dissipation, Lyapunov exponent, Poincar\'{e} diagram and bifurcation diagram. A new finite-time convergence theorem is proposed for general chaotic systems. Compared with the existing finite-time control of chaotic systems, the new finite-time controller with fractional index greater than 1 can also realize the finite-time synchronization of financial Duffing-Holms chaotic systems. The validity of the theoretical results is verified by numerical simulation.

Key words: Duffing-Holms model, chaotic system, finite-time synchronization, chaos control, dynamics

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