吸引子
混乱的
离散化
MATLAB语言
常微分方程
计算机科学
龙格-库塔方法
灵敏度(控制系统)
平衡点
应用数学
Python(编程语言)
欧拉法
微分方程
数学
数值积分
分歧(语言学)
解算器
控制理论(社会学)
欧拉公式
数学分析
数学优化
人工智能
控制(管理)
语言学
哲学
电子工程
工程类
操作系统
作者
Wafaa S. Sayed,Sara M. Mohamed,Ahmed S. Elwakil,Lobna A. Said,Ahmed G. Radwan
标识
DOI:10.1142/s0218127422501036
摘要
We introduce a new chaotic system with nonhyperbolic equilibrium and study its sensitivity to different numerical integration techniques prior to implementing it on an FPGA. We show that the discretization method used in numerically integrating the set of differential equations in MATLAB and Mathematica does not yield chaotic behavior except when a low accuracy Euler method is used. More accurate higher-order numerical algorithms (such as midpoint and fourth-order Runge–Kutta) result in divergence in both MATLAB and Mathematica (but not Python), which agrees with the divergence observed in an analog circuit implementation of the system. However, a fixed-point digital FPGA implementation confirms the chaotic behavior of the system using Euler and fourth-order Runge–Kutta realizations. Therefore, the increased sensitivity of chaotic systems with nonhyperbolic equilibrium should be carefully considered for reproducibility.
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