基于三角函数迭代的吸引子图形研究

Research on attractor graphs based on trigonometric function iteration

构造了三角函数与随机生成的多项式函数动力系统,采用确定性迭代算法分析系统混沌性并绘制其吸引子分形图.通过反复迭代实验分析动力系统混沌吸引子图形变化条件,发现三维正弦和余弦乘积函数与随机多项式构成的动力系统是混沌的概率非常高,并且迭代可产生众多具有观赏性和实用价值的混沌吸引子,这种构造混沌的方法可应用于混沌理论研究,混沌图像加密和工业设计等领域.

By constructing a dynamical system with trigonometric and randomly generated polynomial functions,a deterministic iterative algorithm is used to analyze the chaotic nature of the system and to plot its attractor fractal graphs.It is concluded that the probability,that a dynamical system consisting of a three-dimensional sine and cosine product function and a random polynomial is chaotic is very high,and that the iterations can produce a number of chaotic attractors which are interesting and of practical value.