How to solve for a dependent system of difference (recursive) equations?

I have the following equations and I need help to solve this problem with MATLAB. I am brand new to MATLAB but I know I need 1 for loop to solve this.

I know my code is wrong, but this is what I have.

L(1) = 250;
P(1) = 5;
A(1) = 100;
cel = 0.012;
cea = 0.009;
cpa = 0.004;
ml = 0.267;
mp = 0;
ma = 0.0036;
b = 7.48;

x = linspace(1,1000);

for t=1:1000
    L(t+1) = b*A(t)*exp(-cea*A(t)-cel*L(t));
    P(t+1) = L(t)*(1-ml);
    A(t+1) = P(t)*(1-mp)*exp(-cpa*A(t))+A(t)*(1-ma);
end

L(t)
P(t)
A(t)

plot(x,A(t+1))

And here are the equations/question:

L(t+1) = bA(t)exp(−(cea)A(t)−(cel)L(t))
P(t+1) = L(t)(1 − µl)
A(t+1) = P(t)(1 − µp)exp(−(cpa)A(t)) + A(t)(1 − µa)

Use MATLAB to solve this system of difference equations with initial conditions L(0) = 250, P(0) = 5, A(0) = 100 and the following parameters: cel = 0.012, cea = 0.009, cpa = 0.004, µl = 0.267, µp = 0, µa = 0.0036, and b = 7.48. Plot the behavior of the adults and larvae under these control conditions and describe the baseline long-term behavior. Be sure you compute enough generations to be confident in your assessment of the long-term behavior.

Any help at all would be wonderful. Thank you!

Answer 1

[Star Strider]

You essentially got everything correct. You need to change the definition of ‘t’ in your loop index, and slightly restate the plot call arguments.

With a couple tweaks, it works:

L(1) = 250;
P(1) = 5;
A(1) = 100;
cel = 0.012;
cea = 0.009;
cpa = 0.004;
ml = 0.267;
mp = 0;
ma = 0.0036;
b = 7.48;

x = linspace(1,1000,250);

for t=1:length(x)-1
    L(t+1) = b*A(t)*exp(-cea*A(t)-cel*L(t));
    P(t+1) = L(t)*(1-ml);
    A(t+1) = P(t)*(1-mp)*exp(-cpa*A(t))+A(t)*(1-ma);
end

L(t)
P(t)
A(t)

figure(1)
plot(x,A)
grid
xlabel('Time (Units)')
ylabel('A (Units)')

[Erin W]

Thank you so much! It runs perfectly. I really appreciate it. :) I'm glad I was just slightly off and not completely lost.

Thanks!

[Star Strider]

My pleasure!

You were quite close. I only made two minor changes.