Systems Biology (Methods in Molecular Biology)

hðu;λÞ:¼uλgðuÞ

and thestabilityproperties are deduced by analyzing its first order

derivative (namely, the first order variation ofhwith respect tou),

that is

dh

du

ðÞ¼u;λ 1 λ

dg

du

ðÞu: ð 10 Þ

Actually, for the particular case of system Eq.7, this approach is

equivalent to the standardspectral analysis(refer to Subheading4,

Note 4). More precisely, if the derivativedhduðÞu;λ is positive, the

0.5 1 1.5 2

0.2

0.4

0.6

0.8

1

u

g(u)

a

b

0.5 1 1.5 2

0.2

0.4

0.6

0.8

u

h(u;1)

h(u;1.75)

h(u;2)

Fig. 8The graphs of the structural functionsgandh.(a) A typical S-shaped functiongwithp¼1andℓ¼1. (b)
The corresponding functionhfor distinct values ofλ(λ¼ 1 dashed,λ¼λc¼1. 75dotted,λ¼ 2 continuous)

114 Chiara Simeoni et al.