You Name It – How Memory and Delay Govern First Name Dynamics
Figure 7
Simulated name dynamics for the toy model.
We have simulated the dynamics of 500 “names” along 130 years, starting from random initial conditions, according to Eq. (3) and (4) with ad = am = 1, n = 20, n1 = 30 and τ = 80. We have shifted each of the time series such that the peak is always at zero and normalized the peak height to unity. While the result is not identical with the detailed features of real name dynamics emphasized in Fig 2a, it does show that both the bell shape and the “wings” appear when a simple logistic growth model includes both delay and memory.