Print the values of parameters if the sequence is convergent, periodic, chaotic, divergent

k=1;

alpha=rand(1)+i*rand(1);
beta=rand(1)+i*rand(1);
gamma=rand(1)+i*rand(1);%

s=50000;
Zarray = zeros(1,s);
Zarray(1:k+1)=rand(1,1,k+1)+i*rand(1,1,k+1);

for n=k+1:s-1
   Zarray(n+1) =(alpha+(beta*Zarray(n-k)))/(gamma-Zarray(n));
end

Now the sequence

Zarray is generated.

I want to plot alpha, beta and gamma for which Zarray is converged to a fixed point.

I want to plot alpha, beta and gamma for which Zarray is divergent.

I want to plot alpha, beta and gamma for which Zarray is periodic.

I want to plot alpha, beta and gamma for which Zarray is chaotic (none of the element of the sequence is same to other).

Can anyone help me to make the rest of the code? I need help. I am unable to do it.