% iterates Leslie matrix

n_zero=[10 100 500]' ;

A=[0  1 5 ;
  .5  0 0 ;
  0 .25 0 ];


Tmax=200;

n_vs_t=zeros(3,Tmax);

n_vs_t(:,1)=n_zero ;

for t=2:Tmax;
   n_vs_t(:,t)=A*n_vs_t(:,t-1) ;    
end

figure
set(gca,'FontSize',20)
plot(1:Tmax,n_vs_t','.-','MarkerSize',14)
xlabel('t','FontSize',20)
ylabel('n','FontSize',20)

figure
set(gca,'FontSize',20)
plot(1:Tmax,log(n_vs_t'),'.-','MarkerSize',14)
xlabel('t','FontSize',20)
ylabel('log(n)','FontSize',20)

eig(A)