非线性系统手册源代码集合包括神经网络、混沌映射、元胞自动机、遗传算法、模糊逻辑等

算法采用斜帐篷混沌映射函数初始化种群"在每次迭代中为每个个体分别产生满足正态分布!柯西分布的杂交概率和满足正态分布的缩放因子"并且记录成功变异个体的杂交概率和缩放因子"引入统计杂交概率"采用两种策略自适应地更新杂交概率。

包含了Chebyshev、Circle、Gauss、Iterative等十种混沌映射方式，亲测有效

这个是混沌映射logistic模型的分布图，当U=4的时候，真正的伪随机序列

With the increasing requirements of the performance in secure communication filed based on chaos, chaotic systems have been gradually developed into higher dimensions. Because the sequence generated by onedimension chaos, such as Chebyshev map has the problem of weak chaotic properties and uneven distribution, a new two-dimensional chaotic map, called Logistic-Adjusted-Chebyshev map (2D-LACM), is proposed in this paper which enlarges the range of chaotic control parameter, and expands the range of surjection to the entire control parameter interval to make the distribution of the sequence more uniform. Compared with other improved chaotic maps, the proposed 2D-LACM in this paper has more complex chaotic properties and better ergodicity. Next, a visualized image encryption algorithm based on 2D-LACM is proposed (LACM-VIEA), which can encrypt the plain image into a noisy image, and then embed it into a cover image of the same size. In order to demonstrate the security of LACM-VIEA, the algorithm is analyzed in detail from the aspects of key, histogram, visual effect, robustness and anti-plaintext attacks, etc. The final analysis results show that LACM-VIEA has good security performance.

10个混沌映射的函数表达式及画图matlab代码

一维Logistic映射从数学形式上来看是一个非常简单的混沌映射，早在20世纪50年代，有好几位生态学家就利用过这个简单的差分方程，来描述种群的变化。

研究图像加密问题，水印预处理是其重要内容，它决定整个水印系统稳健性和安全性。传统的水印预处理多采用改变图像某些像素点坐标位置方法，往往形式单一，破解较易而且难以满足控制要求。针对上述问题，本文提出结合Arnold变换与Logistic混沌映射，对水印信息进行混合编码算法，通过小波变换分解载体图像，得到高频子带，将混合编码的水印信息嵌入高频部分，实现水印的嵌入与提取，经过仿真实验，表明该算法不仅具有较好的不可见性和较强的鲁棒性，并且易于实现，为多重水印信号的预处理提供了一种可行的方法。

针对现有灰度图像加密方法的不可逆性，通过引入由简单混沌映射产生的随机矩阵降低了计算复杂度，同时仍保持很好的有效性和安全性。提出的方法成功地解决了现有灰度图像加密方法的不可逆问题，并且该方法能够抵抗Hermassi等人提出的攻击方法。

适用于图像加密研究，非常好的算法。请大家借鉴。