Matlab histogram 画出十二种常见的混沌映射

1
2
3
4
5
   在群体智能优化算法中，需要随机产生数组，然而往往效果并不好。
   由于混沌序列具有非线性、遍历性和不可预测性等特点，因此随机数组可用混沌映射来替代。
   参考 Yu Y ,  Gao S ,  Cheng S , et al. CBSO: a memetic brain storm optimization with chaotic local search[J]. Memetic Computing, 2017.
   相关参数设置可见其论文，不在此赘述。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
clear;
clc;
%% Logistic
y_1=zeros(1,10^5);
y_1(1)=0.152;   
mu=4;
for i = 1 : 10^5-1
    y_1(i+1)=mu*y_1(i)*(1-y_1(i));
end
%% Tent
y_2=zeros(1,10^5);
y_2(1)= 0.152;   
Beta = 0.4;
for i = 1 : 10^5-1   
       if (y_2(i)<=Beta && y_2(i)>0)
          y_2(i+1) = y_2(i)/Beta;
       else 
          y_2(i+1)=(1-y_2(i))/(1-Beta);
       end    
end
%% Cubic
y_3=zeros(1,10^5);
y_3(1)= 0.242;   
rho = 2.59;
for i = 1 : 10^5-1   
    y_3(i+1) = rho*y_3(i)*(1-y_3(i)^2);
end
%% Bernoulli
y_4=zeros(1,10^5);
y_4(1)= 0.152;   
lambda = 0.4;
for i = 1 : 10^5-1   
       if (y_4(i)<=(1-lambda)) && ((y_4(i)>0))
          y_4(i+1) = y_4(i)/(1-lambda);
       else 
          y_4(i+1)=(y_4(i)-1+lambda)/lambda;
       end    
end
%% PWLCM
y_5=zeros(1,10^5);
y_5(1)= 0.002;   
P = 0.7;
for i = 1 : 10^5-1   
       if (y_5(i)<P && y_5(i)>0)
          y_5(i+1) = y_5(i)/P;
       else 
          y_5(i+1)=(1-y_5(i))/(1-P);
       end    
end
%% Singer
y_6=zeros(1,10^5);
y_6(1)= 0.152;   
mu_1 = 1.073;
for i = 1 : 10^5-1   
          y_6(i+1) = mu_1*(7.86*y_6(i)-23.31*y_6(i)^2+28.75*y_6(i)^3-13.302875*y_6(i)^4);
end
%% Sine
y_7=zeros(1,10^5);
y_7(1)= 0.152;   
a = 4;
for i = 1 : 10^5-1   
          y_7(i+1) = a/4*sin(pi*y_7(i));
end
%% Gaussian
y_8=zeros(1,10^5);
y_8(1)= 0.152;   
mu_2 = 1;
for i = 1 : 10^5-1
    if (y_8(i)==0)
        y_8(i+1) =0 ;
    else
        y_8(i+1) =(rem(mu_2/y_8(i),1)) ;
    end
end
%% Chebyshew
y_9=zeros(1,10^5);
y_9(1)= 0.152;   
phi = 5;
for i = 1 : 10^5-1
    y_9(i+1) =cos(phi*acos(y_9(i))) ;
end
%% Circle
y_10=zeros(1,10^5);
y_10(1)= 0.152;   
a_1 = 0.5;
b_1 = 2.2;
for i = 1 : 10^5-1
    y_10(i+1) = y_10(i)+a_1-mod(b_1/(2*pi)*(sin(2*pi*y_10(i))),1);
end
%% Sinusoidal
y_11=zeros(1,10^5);
y_11(1)= 0.74;   
a_2 = 2.3;
for i = 1 : 10^5-1
    y_11(i+1) = a_2*y_11(i)^2*sin(pi*y_11(i));
end
%% ICMIC
y_12=zeros(1,10^5);
y_12(1)= 0.152;   
a_3 = 70;
for i = 1 : 10^5-1
    y_12(i+1) = sin(a_3/y_12(i));
end
%% 画图
subplot(3,4,1)
h1=histogram(y_1,200);
h1.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Logistic map')

subplot(3,4,2)
h2=histogram(y_2,200);
h2.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Tent map')

subplot(3,4,3)
h3=histogram(y_3,200);
h3.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Cubic map')

subplot(3,4,4)
h4=histogram(y_4,200);
h4.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Bernoulli map')

subplot(3,4,5)
h5=histogram(y_5,200);
h5.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('PWLCM map')
subplot(3,4,5)
h5=histogram(y_5,200);
h5.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('PWLCM map')

subplot(3,4,6)
h6=histogram(y_6,200);
h6.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Singer map')

subplot(3,4,7)
h7=histogram(y_7,200);
h7.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Sine map')

subplot(3,4,8)
h8=histogram(y_8,200);
h8.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Gaussian map')

subplot(3,4,9)
h9=histogram(y_9,200);
h9.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Chebyshew map')

subplot(3,4,10)
h10=histogram(y_10,200);
h10.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Circle map')

subplot(3,4,11)
h11=histogram(y_11,200);
h11.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('Sinusoidal map')

subplot(3,4,12)
h12=histogram(y_12,200);
h12.FaceColor=[0 0 1];
xlim([0,1])%设置x轴范围
xlabel('ICMIC map')