基于龙格库塔算法和可编程门阵列技术的混沌系统实现

Implementation of a Chaotic System Based on Runge-Kutta Algorithm and Programmable Gate Array Technology

提出了使用硬件描述语言(HDL)在现场可编程逻辑门阵列器件(FPGA)上实现二阶龙格库塔法产生混沌信号的一种新方法.首先,根据二阶龙格库塔算法分解求解连续混沌系统,得到一个迭代求解过程;其次,使用HDL描述状态机实现该迭代过程,输出数字混沌序列;最后,将数字混沌序列输出至高速数模转换器(DAC),可观察到模拟混沌信号.给出了网格状多卷波混沌系统和经典Lorenz系统上的具体实现步骤和相应结果.结果表明,此方法具有一定的普适性,可用于其它混沌系统的混沌信号产生,且消耗FPGA资源不多,具有很强实用性.

A new approach is proposed in this paper for the hardware implementation of chaotic-signal-generation on field programmable gate array（FPGA） by the hardware description language（HDL） and the second order Runge-Kutta algorithm.Firstly,using the second order Runge-Kutta algorithm,the solution of continuous chaotic systems can be divided into a series of iteration steps.Secondly,using HDL and the state machine method,these iteration steps are implemented to generate digital chaotic sequences.Finally,using the high-speed digital-to-analog converter（DAC）,a continuous analog chaotic signal can be observed.As examples,the detailed steps of realization and corresponding experimental results of a grid multi-scroll chaotic system and a classic Lorenz system are given.This method can be applied to generate chaotic signals of other systems,and do not need many FPGA resources.