Interesting diagram found here: http://www.nature.com/srep/2014/140912/srep06355/fig_tab/srep06355_F2.html
Think of the Horizontal values as CO2 levels and the Vertical values as the resulting temperature. GCMs seem to be modelling the 0.5 and 0.9 result. It’s possible what is actually happening is 1.1 and/or 1.5. The boundary hitting times can be thought of as the control parameter. I’d guess 1.1 is more likely.
Above from the same linked paper. c) reminds me of Tsonis 2007 and Synching. Cycles as in d) might be primarily time dependent, with c) being more complicated. Sometimes you get a regime swap and sometimes you don’t. Comparing synching to cycles during a prolonged glacial period, with cycles the answer is wait X amount of years. With synching, I’d suggest multiple (thousands of) attempts are made to synch and they all fail except the last one.
Now consider that ‘q’ may slowly change over time. And that we could see elements of all three situations blended and changing in the data.