Scholarlink

<p>To efficiently compute the Lyapunov exponent (LE) of fractional differential equations, this study systematically investigates the effects of decomposition terms and iteration step sizes based on the Adomian decomposition method. Several classical systems are analyzed, with the QR method employed to calculate LEs under varying numbers of decomposition terms and step sizes. The results indicate that for constructing chaotic attractor trajectories in three-dimensional and four-dimensional fractional chaotic systems, the optimal number of decomposition terms is three, with a recommended iteration step size of <i>h</i> = 0.001 or smaller. Furthermore, when determining the minimal order of the simplified fractional Lorenz chaotic system, three decomposition terms yield the most accurate LE values. These findings are significant for improving the efficiency and accuracy of LE computation, accurately capturing the dynamic characteristics of complex systems, reducing computational time, and enhancing overall computational efficiency.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

What is the lowest cost to calculate the Lyapunov exponents from fractional differential equations?

  • 期刊论文

  • 发表日期：

    2025年3月7日

查看全文
  • Shuang Zhou,
  • Qiyin Zhang,
  • Shaobo He,
  • Yingqian Zhang

摘要

To efficiently compute the Lyapunov exponent (LE) of fractional differential equations, this study systematically investigates the effects of decomposition terms and iteration step sizes based on the Adomian decomposition method. Several classical systems are analyzed, with the QR method employed to calculate LEs under varying numbers of decomposition terms and step sizes. The results indicate that for constructing chaotic attractor trajectories in three-dimensional and four-dimensional fractional chaotic systems, the optimal number of decomposition terms is three, with a recommended iteration step size of h = 0.001 or smaller. Furthermore, when determining the minimal order of the simplified fractional Lorenz chaotic system, three decomposition terms yield the most accurate LE values. These findings are significant for improving the efficiency and accuracy of LE computation, accurately capturing the dynamic characteristics of complex systems, reducing computational time, and enhancing overall computational efficiency.