Figure 1.
Adoption-only dynamics with different initial conditions.
(A) The normal distribution with unit variance [Eq. (7)]. (B) The box distribution defined on [Eq. (8)].
Figure 2.
Shape of a traveling wave [Eq. (12)] resulting from Fisher's equation.
(A) at
with
. The solid vertical line is the mean, and the dotted vertical line is the mode of the pdf. (B) Temporal pattern of adopting an innovation
with
and
. The solid (red) curve
shows how the fraction of the population with
changes over time, whereas the dotted (green) curve
shows the fraction that has adopted
as a function of time. The solid vertical line is the mean adoption time
, and the dotted vertical lines represent
,
, and
, respectively, to distinguish the five adopter categories.
Figure 3.
Comparison of Eq.(12) with empirical data.
(A) Cumulative number of publications on the diffusion of innovations, excerpted from Ref. [9]. The curve is obtained by fitting a functional form [see Eq. (12)] to the data points where
is the saturation number at
. The fitting parameters are
. (B) The same data shows larger deviations when fitted with the logistic function
(green) or the error function
(blue). Their best fitting parameters are
and
, respectively. (C) Broadband penetration rates in Greece and the United Kingdom (UK) from Eurostat [22]. The curves were obtained in the same way as above with Eq. (12), yielding
for Greece and
for the UK.
Figure 4.
Summary innovation index (SII) versus the rates of adoption in the European Union (EU) member countries.
Table 1.
Fitting results of Eq. (12) to the broadband penetration rates from 2002 to 2010 in EU member countries.