@acer 

Firstly, thank you for the interesting procedure and for for the reference document - this is very interesting (and useful!).

Now, the Maple procedure concerns the standard-form of the logistic recurrence relation and gives the plot ... which is all fine. If we wish to determine the location of the bifurcation points, we can do so analytically as well as from the diagram.

I wish to modify the logistic equation by including an exponent ... as follows:

x(n+1)=rx(n)(1-x(n)^k)

Here, k is a positive rational number and is the index of x(n). This will produce a different logistic diagram and the bifurcation points can be approximated using the map (or using some numerical procedure).

My question is this ... can the current Maple procedure calculate (and output the coordinates of) the location of the bifurcation points (r, x) in addition to producing the bifurcation diagram for any given value of k?

Thanks again for your quick response and assistance!

@sand15 

Very useful insights - thanks for providing this!

@vv 

I appreciate this! Thank you.

@Carl Love 

That did the job! 

I really appreciate this approach .. very impressive.

Thanks again, Carl.

@dharr 

This is exactly whay I need .. thanks for sharing this impressive procedure! I'm grateful.

@mmcdara 

Thank you for your suggestion .. I appreciate the reply.

However, I did try that initially and it did not affect the solution. Perhaps it is (currently) not possible to return such a requirement.

Thanks again!

@Scot Gould 

Thanks for this, Scot. 

It is indeed useful to me. This is an interesting problem I am exploring and these insights provided are great to get.

@rcorless 

Thanks for the timely reply and guidance. I find your advice very beneficial and I'll explore this approach with interest!

@dharr 

Thanks for confirming this .. I'll continue exploring this problem using the routines you provided.

Thank you for this - it is most helpful and I have learned a lot in the process. 

Yes .. I should have stated that both a and b are non-integers. 

Do you think that it is possible to extract a general expression for the roots of f (or g) in terms of a and b?

In the meantime, I will use your model to explore the (real) numerical solutions.

Interesting ...  it seems that your adjustment has resolved the problem .. thank you!

I didn't think about the followup process -  your advice is appreciated.

Thanks for the timely response.

As regards the expected values ...

Parameter a will typically take the value 0.1 and the index, m, will vary from 0.1 to 10

I'll take a look at the commands you suggested - so that will be helpful.

I appreciate your help!

@Carl Love 

Thanks so much for taking an interest in this and for providing me exactly what I need!

@jganding 

That's exactly what I was looking for!

Thanks for the quick response and the advice - especially on the use of the printf command.

I'm very grateful ..

@mmcdara 

I agree. Following your response, I reviewed the references you recommended and they are very interesting indeed.

Once again .. thanks for your help.