基于现场可编程逻辑门阵列的新型混沌系统实现

构建了一个新的五维变形蔡氏系统,通过数值仿真,分析平衡点的稳定性、分岔图和Lyapunov指数谱,研究系统特有的基本非线性动力学行为,还分析了改变不同参数时系统动力学行为的变化.基于混沌系统的数值仿真分析以及数字化处理技术,将五维变形蔡氏系统状态方程进行离散化处理,并根据IEEE-754标准和模块化设计理念构建出实现混沌系统变量运算关系的基本模块,进一步利用现场可编程逻辑门阵列硬件平台实现了五维变形蔡氏系统的混沌吸引子.研究结果表明,新五维变形蔡氏系统具有新的混沌动力学行为,并通过硬件证实了新系统的存在性和物理上的可实现性.

Implementation of a new chaotic system based on field programmable gate array

A new five-dimensional modified Chua’s system is proposed and its dynamic properties are investigated through numerical simulations, the stabilization of equilibrium points, bifurcation diagrams, and Lyapunov exponent spectrum. The different dynamic behaviors of the new system are analyzed with system parameters changed. Based on the mathematical model of the new system and the digital processing technology, the five-dimensional modified Chua’s system is discretized. According to IEEE-754 standard and module-based design idea, basic floating-point operational modules are designed. Furthermore, the chaotic attractors of the five-dimensional modified Chua’s system are realized by field programmable gate array. The investigation results show that the chaotic system is different from the existing chaotic systems. It also shows a good agreement between numerical simulation and hardware implementation, which proves the existence and realizability of the new chaotic system.
Keywords： chaotic system dynamical behavior field programmable gate array implementation