Logistic映射又称为抛物线映射,本文,用python来研究Logistic映射过程中的稳定状态。
工具/原料
电脑
python3.6(Anaconda)
方法/步骤
1、自定义函数如下图:defpaowuxian(d,x,n):……defxunhuanjie(d,x,n):……
2、当系数d为3.5,初始值为0.99999水貔藻疽,而精度控制在小数点后5位有效数字,那么Logistic映射的稳定状态,是周期为4鹚兢尖睁的循环状态:[0.87499,0.38283,0.82694,0.50088]
3、当系数变为3.6的时候,稳定周期是18:职邗珩垃[0.87189,0.40211,0.8655,0.41907,0.87642,0.3899,0.85636,0.44282,0缕计瓤账.88822,0.35742,0.82681,0.5155,0.89913,0.3265,0.79163,0.59382,0.86831,0.41165]
4、同样是系数保持为3.6,把精度提高到7,稳定周期变为98:
5、系数变为3.53的时候,稳定周期变为8:[0.88147龀音孵茧17,0.368812,0.821747鲂番黟谊6,0.517069,0.8814715,0.3688126,0.8217482,0.5170676]
6、把精度提高到15,稳定周期仍旧是8:
7、系数为3.57,精度为5,初始值为0.99999,那么,稳定周期是64:
8、系数为3.561,初始值为0.99999,精度为7的Logistic映射的稳定周期是8。
9、系数为3.562,初始值为0.99999,精度为7的Logistic映射的稳定周期是16。