如题，最基本的分岔概念如：saddle-node；transcritical；supercritical pitchfork；subcritical pitchfork等，如果你不是很了解，可以学习一下下面的程序。
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- %% Animation for a Saddle Node bifurcation
- % Range of x
- xmin = -4;
- xmax = 4;
- x = xmin:0.1:xmax
- % Some auxiliary variable to plot x-axis
- ax = (0.0).*x;
- % Range of r
- rmin = -4
- rmax = 4
- % number of frames in the movie
- imax = 21
- % Rage of dx/dt (here y=dx/dt)
- ymin = rmin ;
- ymax = rmax + xmax.^2;
- % Some auxiliary variables to plot the y-axis
- ky = ymin:0.1:ymax
- ay = (0.0).*ky
- %% Start of the loop for acquisition of the movie frames
- for i = 1:imax
- %calculate r value
- r = rmin + (i-1)*(rmax-rmin)/(imax-1)
- %create string for labelling r
- strr = num2str(r);
- strt = ['r=' strr];
- %calculate dxdt
- y = r + x.^2
- %plot x-axis
- plot(x,ax,'--');
- % determine range of plot
- axis([xmin xmax ymin ymax])
- hold on
- %plot y-axis
- plot(ay,ky,'--')
- %plot f(x)
- plot(x,y,'r');
- %plot fixed points
- if (r < 0)
- plot(-(-r).^(0.5),0,'o','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- plot((-r).^(0.5),0,'o','MarkerSize',10,'MarkerEdgeColor','k');
- end
- if(r == 0.0)
- plot((-r).^(0.5),0,'*','MarkerSize',10,'MarkerEdgeColor','k');
- end
- %plot flow direction
- if(r < 0)
- plot(-3,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- plot(0,0,'<','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- plot(3,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- end
- if(r == 0)
- plot(-3,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- plot(3,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- end
- if(r > 0)
- plot(-3,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k'); plot(0,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- plot(3,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
- end
- %plot labels
- xlabel('x','FontSize',20)
- ylabel('dx/dt','FontSize',20)
- text(-3,15,'dx/dt = r + x^2','Color','r','FontSize',20)
- text(1,15,strt,'FontSize',20)
- title('Saddle Node Bifurcation','FontSize',20)
- %get movie frame
- h = gcf;
- M(i) = getframe(h,[5 5 480 380]);
- hold off
- % end of loop
- end
- %play and save movie
- movie(M);
- movie2avi(M,'SaddleNode','fps',1);
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