Why are my plots for K values and initial conditions all the same colour even with hold on

% Mesh Grid in (Diamtoms(D),Zooplankton(P))-plane
[D, P] = meshgrid(-0.8:1:10, -0.8:1:10);
% Parameters
hold on 
for K=1:10;
    
    s=1;
    e=1;
    r=1;
    H=1;
    d=0.75;
    % System as a 2-D function
    f = @(t,X) [X(1)*(r*(1-X(1)*(1/K))-(s*X(1)/1+s*H*X(1))*X(2)); 
        X(2)*(e*(s*X(1))/(1+s*H*X(1))-d)];
    %Direction Filed
    % Ddot is dD/dt and Pdot is dP/dt derivatives
    Ddot = D-(1./K).*D.*D-(s*D)./((1+s.*H.*D)).*P;
    Pdot = P.*((s.*D)./(1+s.*H.*D))-P.*d;
    % Vector Field
    figure(1)
    quiver(D,P,Ddot,Pdot,'k','LineWidth',1.5)
    timespan=[0 100];
    % Phase Trajectories
    X0=0.5*K*rand;Y0=K*rand;
    [ts, Xs] = ode45(f,timespan, [X0, Y0]);
    % plot of several trajectories
    plot(Xs(:,1), Xs(:,2),'k', 'Linewidth', 2)
    xlabel('Prey, D', 'FontSize',14)
    ylabel('Predator, P', 'FontSize',14)
    set(gca, 'FontSize', 16)
    xlim([-0.8 10])
    ylim([-0.8 10])
end

[Beñat Arribas]

The 'k' defines the color of the plots, which is equivalent to black color. Removing this will turn between the different colors set by default.

quiver(D,P,Ddot,Pdot,'k','LineWidth',1.5)

plot(Xs(:,1), Xs(:,2),'k', 'Linewidth', 2)

Answer 1

[Voss]

They are all the same color because you have specified them all to be black when you plotted them. The 'k' means black in, e.g.:

quiver(D,P,Ddot,Pdot,'k','LineWidth',1.5)
% ...
plot(Xs(:,1), Xs(:,2),'k', 'Linewidth', 2)

Removing the 'k' gives lines with different colors:

% Mesh Grid in (Diamtoms(D),Zooplankton(P))-plane
[D, P] = meshgrid(-0.8:1:10, -0.8:1:10);
% Parameters
hold on 
for K=1:10;
 
s=1;
e=1;
r=1;
H=1;
d=0.75;
% System as a 2-D function
f = @(t,X) [X(1)*(r*(1-X(1)*(1/K))-(s*X(1)/1+s*H*X(1))*X(2)); 
    X(2)*(e*(s*X(1))/(1+s*H*X(1))-d)];
%Direction Filed
% Ddot is dD/dt and Pdot is dP/dt derivatives
Ddot = D-(1./K).*D.*D-(s*D)./((1+s.*H.*D)).*P;
Pdot = P.*((s.*D)./(1+s.*H.*D))-P.*d;
% Vector Field
figure(1)
quiver(D,P,Ddot,Pdot, 'LineWidth',1.5)
timespan=[0 100];
% Phase Trajectories
      X0=0.5*K*rand;Y0=K*rand;
[ts, Xs] = ode45(f,timespan, [X0, Y0]);
% plot of several trajectories
plot(Xs(:,1), Xs(:,2), 'Linewidth', 2)
xlabel('Prey, D', 'FontSize',14)
ylabel('Predator, P', 'FontSize',14)
set(gca, 'FontSize', 16)
xlim([-0.8 10])
ylim([-0.8 10])
end

[Voss]

Also, you can move those things that don't depend on the value of the variable K out of the for loop:

% Mesh Grid in (Diamtoms(D),Zooplankton(P))-plane
[D, P] = meshgrid(-0.8:1:10, -0.8:1:10);
% Parameters
s=1;
e=1;
r=1;
H=1;
d=0.75;
timespan=[0 100];
Pdot = P.*((s.*D)./(1+s.*H.*D))-P.*d;

figure(1)
hold on 
for K=1:10;
    % System as a 2-D function
    f = @(t,X) [X(1)*(r*(1-X(1)*(1/K))-(s*X(1)/1+s*H*X(1))*X(2)); 
        X(2)*(e*(s*X(1))/(1+s*H*X(1))-d)];
    %Direction Filed
    % Ddot is dD/dt and Pdot is dP/dt derivatives
    Ddot = D-(1./K).*D.*D-(s*D)./((1+s.*H.*D)).*P;
    % Vector Field
    quiver(D,P,Ddot,Pdot, 'LineWidth',1.5)
    % Phase Trajectories
    X0=0.5*K*rand;Y0=K*rand;
    [ts, Xs] = ode45(f,timespan, [X0, Y0]);
    % plot of several trajectories
    plot(Xs(:,1), Xs(:,2), 'Linewidth', 2)
end

xlabel('Prey, D', 'FontSize',14)
ylabel('Predator, P', 'FontSize',14)
set(gca, 'FontSize', 16)
xlim([-0.8 10])
ylim([-0.8 10])

Answer 2

[Les Beckham]

Because you told Matlab to make all of the lines black.

For example, the 'k' in this command means "make the lines black":

plot(Xs(:,1), Xs(:,2),'k', 'Linewidth', 2)

% Mesh Grid in (Diamtoms(D),Zooplankton(P))-plane
[D, P] = meshgrid(-0.8:1:10, -0.8:1:10);
% Parameters
% hold on 

s=1;
e=1;
r=1;
H=1;
d=0.75;

for K=1:10;
    % System as a 2-D function
    f = @(t,X) [X(1)*(r*(1-X(1)*(1/K))-(s*X(1)/1+s*H*X(1))*X(2)); 
    X(2)*(e*(s*X(1))/(1+s*H*X(1))-d)];
    %Direction Filed
    % Ddot is dD/dt and Pdot is dP/dt derivatives
    Ddot = D-(1./K).*D.*D-(s*D)./((1+s.*H.*D)).*P;
    Pdot = P.*((s.*D)./(1+s.*H.*D))-P.*d;
    % Vector Field
    figure(1)
    quiver(D,P,Ddot,Pdot) % <<< removed color and linewidth specification
    hold on % <<< hold on AFTER first plot command
    timespan=[0 100];
    % Phase Trajectories
    X0=0.5*K*rand;
    Y0=K*rand;
    [ts, Xs] = ode45(f,timespan, [X0, Y0]);
    % plot of several trajectories
    plot(Xs(:,1), Xs(:,2)) % <<< removed color and linewidth specification
    xlabel('Prey, D', 'FontSize',14)
    ylabel('Predator, P', 'FontSize',14)
    set(gca, 'FontSize', 16)
    xlim([-0.8 10])
    ylim([-0.8 10])
end