flowsimple.m

function flowsimple

xrange = [-5 5];
yrange = [-5 5];
% xrange = [0 4];
% yrange = [0 4];
rngx = xrange(2) - xrange(1);
rngy = yrange(2) - yrange(1);

[X,Y] = meshgrid(xrange(1):0.1:xrange(2), yrange(1):0.1:yrange(2));

smallarrow = 0;
[x,y] = f5(X,Y);

clf
figure(1)
for xloop = 1:10
    xs = xrange(1) +xloop*rngx/10;
    for yloop = 1:10
        ys = yrange(1) +yloop*rngy/10;
        
        streamline(X,Y,x,y,xs,ys)
        
    end
end
hold on
[XQ,YQ] = meshgrid(xrange(1):1:xrange(2),yrange(1):1:yrange(2));
smallarrow = 0;
[xq,yq] = f5(XQ,YQ);
quiver(XQ,YQ,xq,yq,.2,'r','filled')
hold off

axis([xrange(1) xrange(2) yrange(1) yrange(2)])
set(gcf,'Color','White')


    function [x,y] = f5(X,Y)
        
%         xtmp = X*(1-X^2) - Y;
%         ytmp = X;
          
%           xtmp = Y;     % Double well
%           ytmp = -0.5*Y + X - X.^3;

%           xtmp = X*(1-2*X+Y);
%           ytmp = Y*(1+X-Y);

        
%         xtmp = X.*(1-Y.^3);        % testing dsge
%         ytmp = Y.*(2.5-X);
        
%         xtmp = X.*Y + 1 - 0.5*X;
%         ytmp = Y.*(2 - X);

        xtmp = X.*(3-Y);   % Rabbit sheep
        ytmp = Y.*(2-X);

%         xtmp = Y;
%         ytmp = -X - 0.1*exp(-abs(X)/1)*X.^2;

        
%        c = 1;       % Medio
%        xtmp = -Y + X.*(c - Y.^2);
%        ytmp = X + 1;
        
%         xtmp = X.*(1-2*X+Y);
%         ytmp = Y.*(0.5 + 0.5*X - Y);
        
%         xtmp = Y+0.75*X;
%         ytmp = X.^3-Y-X;
        
        
%         xtmp =X.*(2-X-Y);
%         ytmp  = X-Y;
        
        
%         xtmp = X.*(X-Y);
%         ytmp = Y.*(2*X-Y);
        
        
%        a = 2; b = 2;      % Inward spiral
%         xtmp = Y - a*X;
%         ytmp = -X - b*Y;
        
%         xtmp = -X.^2-Y;
%         ytmp = X;
        
%         xtmp = X.^2 - Y;
%         ytmp = X - Y;
        
        %x = X.*(3-X-2*Y);
        %y = Y.*(2-X-Y);
   
          nrm = sqrt(xtmp.^2 + ytmp.^2);
          
          if smallarrow == 1
              x = xtmp./nrm;
              y = ytmp./nrm;
          else
              x = xtmp;
              y = ytmp;
          end
        
    end     % end f5


end % end flowsimple