Hu Han-Ping, Liu Xiao-Hui, Xie Fei-Long
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China.
Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education, Wuhan 430074, China.
Entropy (Basel). 2019 Apr 26;21(5):437. doi: 10.3390/e21050437.
Time-delay chaotic systems can have hyperchaotic attractors with large numbers of positive Lyapunov exponents, and can generate highly stochastic and unpredictable time series with simple structures, which is very suitable as a secured chaotic source in chaotic secure communications. But time-delay chaotic systems are generally designed and implemented by using analog circuit design techniques. Analog implementations require a variety of electronic components and can be difficult and time consuming. At this stage, we can now solve this question by using FPAA (Field-Programmable Analog Array). FPAA is a programmable device for implementing multiple analog functions via dynamic reconfiguration. In this paper, we will introduce two FPAA-based design examples: An autonomous Ikeda system and a non-autonomous Duffing system, to show how a FPAA device is used to design programmable analog time-delay chaotic systems and analyze Shannon entropy and Lyapunov exponents of time series output by circuit and simulation systems.
时滞混沌系统可以具有带有大量正李雅普诺夫指数的超混沌吸引子，并且能够生成具有简单结构的高度随机且不可预测的时间序列，这非常适合作为混沌安全通信中的安全混沌源。但是时滞混沌系统通常是利用模拟电路设计技术来设计和实现的。模拟实现需要各种电子元件，并且可能既困难又耗时。在现阶段，我们现在可以通过使用现场可编程模拟阵列（FPAA）来解决这个问题。FPAA是一种通过动态重配置来实现多种模拟功能的可编程器件。在本文中，我们将介绍两个基于FPAA的设计示例：一个自治的池田系统和一个非自治的杜芬系统，以展示如何使用FPAA器件来设计可编程模拟时滞混沌系统，并分析电路和仿真系统输出的时间序列的香农熵和李雅普诺夫指数。
