Question

Matlab:

% We are studying a population with juveniles J, youths Y and adults A;

L=[0 .8 2.2; .5 0 0; 0 .6 0] (I relabeled this population matrix with A because it worked better with the exercise I did last week)

% part c) If J_0=25, Y_0=50 and A_0=25, draw plots on the same set of axes
% of the populations of each stage for the first 30 seasons

Under the same initial conditions, plot the natural logarithms % of the populations versus time (in the previous plot commands, % replace the population vector by log(population` vector). Read the answer % in the book to get an explanation of what is happening.

Answer 1

My code attempt

>> clear all;
timesteps=30;
x=[25; 50; 25]; xhistory=x;
A=log([0 .8 2.2; .5 0 0; 0 .6 0]);
for t=1:timesteps;
x=A*x;
xhistory=[xhistory x];
end
>> time=0:timesteps;
subplot(2,1,1)
>> plot(time,xhistory(1,:),'-'),
xlabel('time'), ylabel('populations'),
hold on
>> plot(time, xhistory(2,:))
subplot(2,1,2)
plot(xhistory(1,:), xhistory(2,:)),
xlabel('juveniles'), ylabel('adults'),
hold on
[V,D]=eig(A)
C= V\xhistory(:,1)
xpprox = C(2)*V(:,2)*D(2,2).^(time)


>> subplot(2,1,1)
>> plot(time, xpprox, 'r')
>> subplot(2,1,2)
>> plot(xpprox(1,:),xpprox(2,:),'r')

Answer 2

These two are the graphs without the change the population matrix into a logarithm and plot those. Corresponds to part c.

Answer 3

@Lyrae @dan815

Answer 4

>> clear all;
timesteps=30;
x=[25; 50; 25]; xhistory=x;
A=[0 .8 2.2; .5 0 0; 0 .6 0];
for t=1:timesteps;
x=A*x;
xhistory=[xhistory x];
end
time=0:timesteps;
subplot(2,1,1)
semilogx(time,xhistory(1,:),'-'),
xlabel('time'), ylabel('populations'),
hold on
semilogy(time, xhistory(2,:))
subplot(2,1,2)
plot(xhistory(1,:), xhistory(2,:)),
xlabel('juveniles'), ylabel('adults'),
hold on
>>

Answer 5

Hey, do you still need help with this?