close all
clear all
clc

set(gca,'FontSize',18)
set(gca,'LineWidth',2)
v = 2;

beta = (-0.2:0.1:1.2).';
gamma = (-0.5:0.1:0.5);

beta_matrix =beta*ones(size(gamma));

gamma_matrix =ones(size(beta))*gamma;

u_x = gamma_matrix;

u_y = -v*gamma_matrix - beta_matrix.*(1-beta_matrix);


quiver(beta_matrix,gamma_matrix,u_x,u_y,1,'LineWidth',2)
xlabel('\beta')
ylabel('\gamma')
hold on
plot(1,0,'o','MarkerFaceColor','r','MarkerSize',10)
plot(0,0,'o','MarkerFaceColor','g','MarkerSize',10)
M = [0,1,;1,-2];
[V,D] = eig(M);
r=0.1;
plot_arrow(1,0,1+r*V(1,2),r*V(2,2),...
    'linewidth',2,'headwidth',0.25,'headheight',0.33)
plot_arrow(1,0,1-r*V(1,2),-r*V(2,2),...
    'linewidth',2,'headwidth',0.25,'headheight',0.33)

plot_arrow(1+r*V(1,1),r*V(2,1),1,0,...
    'linewidth',2,'headwidth',0.25,'headheight',0.33)
plot_arrow(1-r*V(1,1),-r*V(2,1),1,0,...
    'linewidth',2,'headwidth',0.25,'headheight',0.33)

axis([-0.2,1.2,-0.5,0.5])

hold off

print -djpeg r_d_phase_portrait
% now we solve for the heteroclinic connection using Euler's method


r=0.0001;
x(1) = 1+r*V(1,2);
y(1) = r*V(2,2);
dt = 0.01;
t(1) = 0;

for j = 1:4000;
    x(j+1) = x(j) + dt*y(j);
    y(j+1) = y(j) + dt*(-v*y(j) - x(j).*(1-x(j)));
    t(j+1) = t(j) + dt;
end

delete r_d_wave.gif
for count = 1:100:length(t)
subplot(2,1,1)
set(gca,'FontSize',18)
set(gca,'LineWidth',2)
quiver(beta_matrix,gamma_matrix,u_x,u_y,1,'LineWidth',2)
xlabel('\beta')
ylabel('\gamma')
hold on
plot(1,0,'o','MarkerFaceColor','r','MarkerSize',10)
plot(0,0,'o','MarkerFaceColor','g','MarkerSize',10)
M = [0,1,;1,-2];
[V,D] = eig(M);
r=0.1;
% plot_arrow(1,0,1+r*V(1,2),r*V(2,2),...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)
% plot_arrow(1,0,1-r*V(1,2),-r*V(2,2),...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)
% 
% plot_arrow(1+r*V(1,1),r*V(2,1),1,0,...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)
% plot_arrow(1-r*V(1,1),-r*V(2,1),1,0,...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)

plot(x(count),y(count),'d','MarkerFaceColor','k','MarkerSize',10)

axis([-0.2,1.2,-0.5,0.5])


plot(x,y,'c','LineWidth',2)
    
hold off

subplot(2,1,2)
set(gca,'FontSize',18)
set(gca,'LineWidth',2)
plot(t,x,'LineWidth',2)
axis([0,40,-0.2,1.2])
xlabel('y')
ylabel('\beta')
hold on
plot(t(count),x(count),'d','MarkerFaceColor','k','MarkerSize',10)
 gif_add_frame(gcf,'r_d_wave.gif',2);
hold off
end