This is fun. You might consider looking into dynamical systems, since this is in effect what you are studying here. The general idea for a dynamical system is that you have some state (x(t),y(t)) whose derivative is given by some function f(x(t),y(t),t) . You can look at the fixed points of such systems, and characterize their behavior relative to these. The notion of bifurcation classifies what happens as you change the parameters in a similar way to what you’re doing There are maybe 2 weird things you’re doing from this perspective. The first is the max function, which is totally valid, though usually people study these systems with continuous and nonlinear functions f(x,y). What you’re getting with it falling into a node and staying is a consequence of the system being otherwise linear. Such systems are pretty easy to characterize in terms of their fixed points. The other weird thing is time dependence; normally these things are given by f(x,y) with no time dependence, called autonomous systems. I’m not entirely clear how you’re implementing the preference decay, so I can’t say too much there.

As for the specific content, give me a bit to read more.

This is fun. You might consider looking into dynamical systems, since this is in effect what you are studying here. The general idea for a dynamical system is that you have some state (x(t),y(t)) whose derivative is given by some function f(x(t),y(t),t) . You can look at the fixed points of such systems, and characterize their behavior relative to these. The notion of bifurcation classifies what happens as you change the parameters in a similar way to what you’re doing

There are maybe 2 weird things you’re doing from this perspective. The first is the max function, which is totally valid, though usually people study these systems with continuous and nonlinear functions f(x,y). What you’re getting with it falling into a node and staying is a consequence of the system being otherwise linear. Such systems are pretty easy to characterize in terms of their fixed points. The other weird thing is time dependence; normally these things are given by f(x,y) with no time dependence, called autonomous systems. I’m not entirely clear how you’re implementing the preference decay, so I can’t say too much there.

As for the specific content, give me a bit to read more.