双指数混沌系统的动力学分析及数字实现

Dynamical Analysis and Digital Realization of a Chaotic System with Dual-exponential

为产生复杂的混沌伪随机信号,在经典的Lorenz系统基础上,设计了含有双指数的混沌系统,其指数项的底数d可在一定范围内任意变化.对此混沌系统的一些基本动力学特性进行了理论分析和数值仿真,如平衡点、平衡点的稳定性、Lyapunov指数谱和分岔图等.利用DSP实现了该混沌系统,并对该系统的伪随机序列进行了NIST测试,结果表明与其它指数混沌系统相比,该系统产生的伪随机序列的随机性良好,在混沌加密应用中有着良好的前景.

For generating complex chaotic pseudo random signals,based on Lorenz system,this paper designs a novel chaotic system with two exponential terms,in which the base of exponential termd can be varied at a certain range.Some basic dynamical characteristics,such as equilibrium points,Lyapunov exponent spectrum and bifurcation diagrams of this system,are analyzed theoretically and simulated numerically.The proposed system is realized by DSP technology and tested by NIST criterion.Results show that proposed system possesses better randomness and complexity for its chaotic sequences compared with other exponent-based chaotic systems,and has good potential applications in chaotic encryptions.