Extended Data Fig. 2: Generalized peak-selection mechanism leads to modularity emergence.
From: Global modules robustly emerge from local interactions and smooth gradients
(a) Energy landscape (Lyapunov function) for dynamics of the abstract state variable x consisting of a rugged multi-minimum function and a smooth, broad single-minimum function with minimum located at x*. (b) As a parameter θ is varied, x* varies as g(θ), where g is some monotonic function. (c) The resulting fixed points \(\bar{x}\), as a function of the smoothly varied θ, form sets with a constant value, followed by an abrupt jump to a new set of values, and so on in a series of discrete steps, defining a set of discrete modules. (See SI Sec. I for simulation details).
