绘制庞加莱截面图.m

Poincare映射图像有不同的做法

% Poincare_section[绘制庞加莱截面图] 
betaa=0.25; 
F=1.093; 
v=2/3; 
Poin=inline(['[x(2);',... 
       '-2*betaa*x(2)-x(2).^2.*sin(x(1))+F*cos(v*t);',... 
       'v]'],... 
       't','x','flag','betaa','F','v'); 
% Poincare_section[绘制庞加莱截面图] 
[t,x]=ode45(Poin,[0,2800],[0,1.5,0],[],betaa,F,v); 
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);