Irreducible Chaotic Polynomials

mgeile

I'm working to generate discrete chaotic sequences - directly in an algebraic field. In a reference:

Digital Chaotic Communications by Alan Michaels https://smartech.gatech.edu/bitstream/handle/1853/34849/michaels_alan_j_200908_phd.pdf

I come across the term "irreducible chaotic polynomials". The reference provides several example polynomials, but does not define it nor characterize it. I'd like to be able to pull my own polynomials; as much as literature can support anyway.

A given example (p25):

$f(x) = 3x^3 + 3x^2 + x + 7$ over GF(11)

To start, I can identify "irreducible polynomials over a finite field". But I cannot find reference to "irreducible chaotic polynomials", even to identify a definition, much less motivate construction and characterization. Can anyone provide guidance (maybe a reference) to where I can access definition and identification of these over general finite (integer) fields?