lotkavoltstream.m

% function lotkavoltstream
%


function lotkavoltstream

alpha = 1;
beta = 1.5;
gamma = 1.;
delta = 1.25;

figure(1)
N = 20;
for loop = 2:N
    
    xstar = gamma/delta;
    ystar = alpha/beta;
    
    valx = xstar*loop/N;
    valy = ystar*loop/N;
    y0 = [valx valy];
    tspan = [0 10];
    [t,y] = ode45(@F5,tspan,y0);
    [sz dum] = size(t);
    y0 = [y(sz,1) y(sz,2)];
    clear t y
    tspan = [10 20];
    options = odeset('RelTol',1e-7);
    [t,y] = ode45(@F5,tspan,y0,options);
    
    plot(y(:,1),y(:,2),'LineWidth',1.5)
    mxlim = 3*max(xstar,ystar);
    axis([0 mxlim 0 mxlim])

    hold on
    
end
hold off
set(gcf,'Color','white')


figure(2)
N = 3;
for loop = 2:N
    
    xstar = gamma/delta;
    ystar = alpha/beta;
    
    valx = xstar*(loop-1)/N;
    valy = ystar*(loop-1)/N;
    y0 = [valx valy];
    tspan = [0 10];
    [t,y] = ode45(@F5,tspan,y0);
    [sz dum] = size(t);
    y0 = [y(sz,1) y(sz,2)];
    clear t y
    tspan = [10 40];
    options = odeset('RelTol',1e-7);
    [t,y] = ode45(@F5,tspan,y0,options);
    
    plot(t,y(:,1),t,y(:,2),'--','LineWidth',1.5)
    mxlim = 3*max(xstar,ystar);

    hold on
    
end
hold off
set(gcf,'Color','white')





%keyboard

    function [x,y] = f5(X,Y)
        
        
        x = X.*(alpha - beta*Y);
        y = -Y*(gamma - delta*X);
        
        
    end     % end f5

    function yd = F5(t,y)
        
        yp(1) = y(1).*(alpha - beta*y(2));
        yp(2) = -y(2).*(gamma - delta*y(1));
        
        
        yd = [yp(1);yp(2)];
        
    end     % end f5


end % end flowsimple