function fig62 % solve IVP using MATLAB routines % y' = f(t,y) with y(0) = y0 % where y = (y1, y2, y3 , ..., yn) is an n-vector % clear all previous variables and plots clear * clf % get(gcf) set(gcf,'Position', [805 516 578 232]); hold on for i=1:2 % time interval tmax=20; if i==1 y10=0; y20=1; y0=[y10 y20]; i1=30; ii1=i1+1; i2=50; ii2=i2+1; else y10=2; y20=0; y0=[y10 y20]; i1=30; ii1=i1+1; i2=50; ii2=i2+1; end % calculate solution using a MATLAB routine [t,y] = ode45(@rhs,[0 tmax],y0); %[t,y] = ode23s(@rhs,[0 tmax],y0); plot(y(:,1),y(:,2),'k') arrowhead([y(i1,1) y(ii1,1)],[y(i1,2) y(ii1,2)],'k',[1.4 1.6]); arrowhead([y(i2,1) y(ii2,1)],[y(i2,2) y(ii2,2)],'k',[1.4 1.6]); end; axis([-1.5 2 -2 1]); % commands to label each axes xlabel('y-axis','FontSize',14,'FontWeight','bold') ylabel('v-axis','FontSize',14,'FontWeight','bold') grid on % command to put legend into plot %legend(' y_1',' y_2',4); % have MATLAB use certain plot options (all are optional) box on % Set the fontsize to 14 for the plot set(gca,'FontSize',14); % Set legend font to 14/bold set(findobj(gcf,'tag','legend'),'FontSize',14,'FontWeight','bold'); hold off % define f(t,y) function dy=rhs(t,y) dy=zeros(2,1); b=0.25; lam=1; dy(1) = y(2); dy(2) = -2*b*y(2) + lam*y(1) - y(1)^3;