Henon映射

最新推荐文章于 2024-04-16 20:43:40 发布

原创最新推荐文章于 2024-04-16 20:43:40 发布 · 824 阅读

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#学习

本文展示了如何使用Matlab编程语言通过Henon映射算法生成一系列二维散点图，展示了参数a和b的变化对序列x(n)的影响，揭示了当参数超出一定范围时可能出现的混沌行为。

Henon映射的数学表示为：

clear,clc
%% when a =0.5,b=0.05
a = 0.5;
b = 0.05;
x(1) = 0;
y(1) = 0;
for i = 2:2000
    x(i) = y(i-1) - a*x(i-1)^2 +1;
    y(i) = b.*x(i-1);
end
subplot(2,2,1)
scatter(x,y)
txt = {'a = 0.5','b= 0.05'};
text(0.1,0.04,txt)

set(gca,'xlim',[min(x),max(x)])
xlabel('n');
ylabel('x(n)');
%% when a=1,b=0.05
a = 1;
b = 0.05;
x(1) = 0;
y(1) = 0;
for i = 2:2000
    x(i) = y(i-1) - a*x(i-1)^2 +1;
    y(i) = b.*x(i-1);
end
subplot(2,2,2)
scatter(x,y)
txt = {'a = 1','b= 0.05'};
text(0,0.04,txt)

set(gca,'xlim',[min(x),max(x)])
xlabel('n');
ylabel('x(n)');
%% when a=1.2,b=0.1
a = 1.2;
b = 0.1;
x(1) = 0;
y(1) = 0;
for i = 2:2000
    x(i) = y(i-1) - a*x(i-1)^2 +1;
    y(i) = b.*x(i-1);
end
subplot(2,2,3)
scatter(x,y)
txt = {'a = 1.2','b= 0.1'};
text(-0.2,0.08,txt)

set(gca,'xlim',[min(x),max(x)])
xlabel('n');
ylabel('x(n)');
%% when a=1.4,b=0.3
a = 1.4;
b = 0.3;
x(1) = 0;
y(1) = 0;
for i = 2:2000
    x(i) = y(i-1) - a*x(i-1)^2 +1;
    y(i) = b*x(i-1);
end
subplot(2,2,4)
scatter(x,y)
txt = {'a = 1.4','b= 0.3'};
text(-1,0.2,txt)

set(gca,'xlim',[min(x),max(x)])
xlabel('n');
ylabel('x(n)');

结果：