(17)
Figure 17. Increase of -.
;/[ ]>⅛min
in athsr сas s
(18)
Figure 18. Decrease of -.
where $ (dalet) determines the length of the divergence and 9 (reysh) determines the speed of
the divergence of - bounded between -min and -max. Expression (17) can be seen as a
hyperbolical divergence from -min, as seen in Figure 17, and expression (18) as a hyperbolical
divergence from -max, as shown by Figure 18. The parameter " in BeCA is adjusted using
similar expressions21 (Gershenson and Gonzalez, 2000). Because of the hyperbolical
divergences, once a -k value reaches the neighbourhood of either -max or -min, it will be
difficult that it will leave the neighbourhood. Therefore, for low values of $ and/or high values
of 9, there is a strong dependence on the initial conditions.
The hyperbolical divergences simulate a persistence of the imitation factor over time,
so that it does not jump linearly every time the individual imitates or not a behaviour. This gives
a smoother transition of the values of -k, and it makes -max and -min to be attractors.
21See Section 3.8.2.
58
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