poincare_section.m.txt

绘制庞加莱截面图的小程序

%matlab计算程序如下: 

% Poincare_section[绘制庞加莱截面图] 
[t,x]=ode45(@Poincare,[0,2800],[0,1.5,0]); 
x(:,2)=mod(x(:,2),2*pi)-pi; 
phi0=pi*2/3; % 选择phi=2*pi/3这个截面 
for k=1:round(max(x(:,3))/2/pi); 
d=x(:,3)-(k-1)*2*pi-phi0; 
[P,K]=sort(abs(d)); 
x1l=x(K(1),1); 
x1r=x(K(2),1); 
x2l=x(K(1),2); 
x2r=x(K(2),2); 
x3l=x(K(1),3); 
x3r=x(K(2),3); 
if abs(P(1))+abs(P(2))<3e-16; 
X1(k)=x1l; 
X2(k)=x2l; 
else 
Q=polyfit([x3l,x3r],[x1l,x1r],1); 
X1(k)=polyval(Q,(k-1)*2*pi-phi0); 
Q=polyfit([x3l,x3r],[x2l,x2r],1); 
X2(k)=polyval(Q,(k-1)*2*pi-phi0); 
end 
end 
plot(X1,X2,'.'); 
xlabel('\theta','fontsize',14); 
ylabel('d\theta/dt','fontsize',14); 


function dx=Poincare(t,x); 
% 单摆方程[不显含时间t的自治系统] 
% 方程如下: 
% dθ/dt=ω, 
% dω/dt=-2*β*[dθ/dt]-ω^2*sin(θ)+F*cos(vt) 
% dψ/dt=v 
betaa=0.25; 
F=1.093; 
v=2/3; 
P2=-2*betaa*x(2)-x(2).^2.*sin(x(1))+F*cos(v*t); 
dx=[x(2)2;v];