在线咨询
中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (5): 835-844.doi: 10.3969/j.issn.1005-3085.2022.05.012

• • 上一篇    下一篇

一个新金融Duffing-Holms模型的动力学分析与控制

赵   玥1,   徐玉华1,   谢承蓉2   

  1. 1. 南京审计大学金融学院，南京 211815；2. 南京审计大学统计与数学学院，南京 211815
  • 出版日期:2022-10-15 发布日期:2022-12-15
  • 通讯作者: 徐玉华 E-mail: yuhuaxu2004@163.com
  • 基金资助:
    国家自然科学基金 (62176127; 61673221)；江苏省“六大人才高峰”项目 (DZXX-019)；江苏省高校自然科学基金(20KJA120002)；江苏省金融工程实验室开放课题 (NSK2021-09)；江苏省高等学校应用经济学优势学科建设项目 ([2018]87)；江苏省研究生培养创新计划项目 (KYCX21-1856).

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).

PDF (PC)

74

摘要： 提出了一个新的金融Duffing-Holms混沌模型，并讨论了该系统的Hopf分岔、耗散性、Lyapunov指数、Poincar\'{e}图和分岔图等基本动力学性质。针对一般的混沌系统，给出了一个新的有限时间收敛定理。一般地，已存在的混沌系统有限时间控制器的分数阶指数介于 0 到 1 之间，而新有限时间控制器的分数阶指数大于 1 也能实现金融 Duffing-Holms 混沌系统的有限时间同步。最后数值模拟验证了理论结果的有效性。

关键词: Duffing-Holms 模型, 混沌系统, 有限时间同步, 混沌控制, 动力学

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

中图分类号: