广义二维多项式混沌映射及其在信息传输中的应用

Generalized 2D polynomial chaotic map and its application in information transmission

现有混沌映射在工程应用中存在许多缺陷,如混沌参数范围不连续、弱混沌、混沌序列输出不均匀和动力学退化等。基于此,提出了一种广义二维多项式混沌映射,通过设定不同控制参数和多项式最高次数,得到一系列特定Lyapunov指数的二维多项式混沌映射。为避免该映射第二个状态方程的输出塌陷为一个固定值,引入了一个不随时间变化的随机扰动变量。然后,通过具体的数值实例验证了该映射的有效性,动力分析表明该映射具有复杂的动力学行为。最后,将该映射应用于信息传输技术,相较于其他混沌映射,该映射可以取得更小的误码率,表明该混沌映射更适用于混沌信息传输。

Existing chaotic systems have many defects in engineering applications,such as discontinuous chaotic parameter range,weak chaos,uneven output of chaotic sequences and dynamic degradation.Therefore,a generalized 2D polynomial chaotic mapping model was proposed.By setting different control parameters and the highest degree of polynomial,a series of 2D robust chaotic maps with specific Lyapunov exponent could be obtained.In order to avoid the output of the second state equation collapsing to a fixed value,a random disturbance variable which did not change with time was introduced.Finally,a numerical example was given to verify the effectiveness of the proposed model,and the dynamic analysis showed that the mapping has complex dynamic behavior.Finally,the system was applied to information transmission technology.Compared with other chaotic maps,the system can achieve lower bit error rate,which indicates that the chaotic map is more suitable for chaotic information transmission.