What are the popular benchmark systems and equations in adaptive signal processing?

In various papers I met repeating equations and systems used during experimental analysis. For example AR model as follows

$x(k) = 1.79 x(k-1) - 1.85 x(k-2) + 1.27 x(k-3) - 0.41 x(k-4) + v(k)$

seems to be kind of popular "linear data generator".

I have few questions related to these popular systems:

1. There is unlimited number of options how to generate data for experiments, why some systems are used repeatedly?

2. Can you provide me some more benchmark systems, with notes/hints/informations why they are popular? Why they are selected by many authors?

3. If I am writing a paper about method, is there any general rule how I should choose/create the data for experiments?

I know this question is really broad, so please feel free to answer just these parts of questions that are answerable according to you. Even that can help me to understand the problem, or reformulate this question or ask more sane question on the topic.

• It'd help to state where you saw this particular process. – Batman Jan 8 '17 at 21:11
• The mackey glass time series, the logistic process... – Brethlosze Jan 8 '17 at 21:51
• I also think this question is broad BUT this is an standard issue everybody face at least once, hence the answer is actually not vague... – Brethlosze Jan 8 '17 at 21:54
• @Batman I saw this process in ieeexplore.ieee.org/document/1261952 and at least two more papers (I think both of them were also IEEE). – matousc Jan 9 '17 at 6:31