How do I overlay multiple logistic population curves on a single plot?

Firstly here is the code I have made to plot a logistic population curve:

% Run logistic dynamics for N generations and plot result
R= 1.6; % goodness/growth parameter
R2 = 0.8
R3 = 9
R4 = 1
n=25; % number of generations
x=[]; % initialise empty list of population values 
x(1) = 0.001; % initial population

for t = 1:n-1
x(t+1) = R*x(t)*(1-x(t)); % logistic dynamics
end
figure(1); clf
plot(x,'b');hold on;
plot(x,'go');hold off;
axis([1 n 0 0.45]); 

title('Example of Logistic Population Dynamics') 
xlabel('Generation number');
ylabel('Population (fraction of max)');
grid on;

Now, i want to vary some factors to see what effect they have on population growth. However, I do not want them on separate plots so could someone explain to me how i can edit my code so i can have multiple logistic population curves on a single plot?

Kind regards and many thanks

Answer 1

[Star Strider]

You may want to change the axis call, but assuming you want to run curves for each value of ‘R’ and plot them on the same plot, this works:

% Run logistic dynamics for N generations and plot result
Rv= [1.6; 0.8; 9; 1]; % goodness/growth parameter
n=25; % number of generations
G = 1:n;

for r = 1:length(Rv)
    R = Rv(r);
    x(r,1) = 0.001; % initial population
    for t = 1:n-1
        x(r,t+1) = R*x(r,t)*(1-x(r,t)); % logistic dynamics
    end
end

figure(1)
plot(G,x(1,:),'b', G,x(1,:),'go');
hold on
for r = 2:length(Rv)
    plot(G,x(r,:),'-', G,x(r,:),'o')
end
hold off;
axis([1 n 0 0.45]); 

title('Example of Logistic Population Dynamics') 
xlabel('Generation number');
ylabel('Population (fraction of max)');
grid on

[Jack Farr]

This is great, thank you for your help!

[Star Strider]

My pleasure!

[Jack Farr]

Hi, I was wondering if you could help me with one last thing?

I have found some really interesting findings overlaying and playing with the growth parameter (Rv) in the re written code you helped with?

I was wondering if you knew how to do the same thing but so I can alternate the starting population instead of the growth parameter (specified above currently as 0.001.

Sorry to have to bother you again, still a beginner at all this!

Many thanks and all the best, Jack

[Star Strider]

I’ll do my best!

To do that, you would use a second for loop, nesting (or nested in) the one for ‘R’.

This works, but some of your data take off to -Inf so you might want to adjust those ‘R’ values:

% Run logistic dynamics for N generations and plot result
Rv= [1.6; 0.8; 9; 1]; % goodness/growth parameter
Pv = [0.001; 0.005];  % Initial Population Vector
n=25; % number of generations
G = 1:n;

for r = 1:length(Rv)
    R = Rv(r);
    for p = 1:length(Pv)
        x(r,p,1) = Pv(p); % initial population
        for t = 1:n-1
            x(r,p,t+1) = R*x(r,p,t)*(1-x(r,p,t)); % logistic dynamics
        end
    end
end

figure(1)
for p = 1:length(Pv)
    Q1 = squeeze(x(:,p,:));
    plot(G,Q1(1,:),'b', G,Q1(1,:),'go');
    hold on
    for r = 2:length(Rv)
        plot(G,Q1(r,:),'-', G,Q1(r,:),'o')
    end
end
hold off;
axis([1 n 0 2.5]); 
grid on

title('Example of Logistic Population Dynamics') 
xlabel('Generation number');
ylabel('Population (fraction of max)');
grid on

[Jack Farr]

This is perfect!

Thanks again, this has been a massive help. I look forwards to having a play with this.

Once again, many thanks. Jack

[Star Strider]

As always, my pleasure!