matlab simulink 求解连续微分系统混沌系统

太过爱你忘了你带给我的痛 2023-02-26 06:28 182阅读 0赞

## 1、常微分方程（Lorenze混沌系统）： ##

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![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70][]

### 方法1：m文件实现 ###

function exam1
    
    x0=[0;0;1e-3];
    [t,x]=ode45(@lorenzfun,[0,100],x0);
    figure(1)
    plot(t,x)
    figure(2)
    plot3(x(:,1),x(:,2),x(:,3))

function dx=lorenzfun(t,x)
    
    a=10;c=28;b=8/3;
    dx=zeros(3,1);
    dx(1)=-b*x(1)+x(2)*x(3);
    dx(2)=-a*x(2)+10*x(3);
    dx(3)=-x(1)*x(2)+c*x(2)-x(3);

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 1][]

### 方法2：Simulink模糊实现 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 2][]

其中三个积分模块的初始值设置与exam1相同，仿真时长为100s。精度设置：Simulation--Configuration Parameters—Relative tolerance, 1e-3改为1e-5（试试不作此修改的结果比较）。运行后双击示波器scope后可看到：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 3][]

在matlab命令窗口输入画图命令：

figure
    plot(tout,yout)
    figure
    plot3(yout(:,2),yout(:,3),yout(:,1))

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 4][]

### 方法3：simulink向量模块 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 5][]

### 方法4：Simulink中S函数的实现 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 6][]

## 2、常时滞微分方程 ##

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 7][]

### 方法1：m文件需调用dde23来求解 ###

function exam2
    
    sol = dde23('exam1f',[1, 0.2],ones(3,1),[0, 5]);
    
    plot(sol.x,sol.y);
    title('Example 2')
    xlabel('time t');
    ylabel('y(t)');

function v = exam1f(t,y,Z)
    ylag1 = Z(:,1);
    ylag2 = Z(:,2);
    v = zeros(3,1);
    
    v(1) = ylag1(1);
    v(2) = ylag1(1) + ylag2(2);
    v(3) = y(2);

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 8][]

### 方法2：Simulink中S函数来实现： ###

注：用Simulink中S函数求解时滞微分方程的核心思想在于：将时滞变量作为S函数的外部输入。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FpbmdmZW5neGQx_size_16_color_FFFFFF_t_70 9][]

## ![20200714173553802.png][] ##

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[20200714173553802.png]: /images/20230209/45b48a33b23b48949ea7061a98f22a9c.png