Scholarlink

<p>In this work, we investigate polynomial approximations of the exponential terms in two well-known chaotic maps: the Chialvo and Ricker maps. By applying Taylor series expansions of varying orders, we analyze how closely the truncated systems replicate the dynamics of the original maps. The chaotic behavior of both the original and approximated systems is examined using classical tools, including bifurcation diagrams, the 0–1 test for chaos, and Lyapunov exponent plots. Through these analyses, we aim to assess the fidelity of the polynomial approximations in capturing the essential dynamical features of the original systems. Additionally, we evaluate the accuracy of the approximations using the root mean square error (RMSE).</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

On Taylor Series Expansion for Discrete Systems Involving Exponential Function and Assessing Their Chaotic Strength

  • 期刊论文

  • 发表日期：

    2026年1月7日

查看全文
  • H. Baranwal,
  • A. K. B. Chand,
  • Sishu Shankar Muni

摘要

In this work, we investigate polynomial approximations of the exponential terms in two well-known chaotic maps: the Chialvo and Ricker maps. By applying Taylor series expansions of varying orders, we analyze how closely the truncated systems replicate the dynamics of the original maps. The chaotic behavior of both the original and approximated systems is examined using classical tools, including bifurcation diagrams, the 0–1 test for chaos, and Lyapunov exponent plots. Through these analyses, we aim to assess the fidelity of the polynomial approximations in capturing the essential dynamical features of the original systems. Additionally, we evaluate the accuracy of the approximations using the root mean square error (RMSE).