
72 Feedback Control in Systems Biology
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x
FIGURE 3.1: Intersections of x/(1 + x
2
) (solid line) and r(1 − x/q) (dashed
lines) for q = 20 and r = 0.15, 0.4, 0.6.
Obviously, x = 0 is an equilibrium point, but so are all the solutions to the
equation
r
1 −
x
q
=
x
1 + x
2
(3.15)
These solutions can be easily visualised by plotting both sides of Eq. (3.15),
as shown in Fig. 3.1: the intersections co rrespond to the equilibrium points
of system (3.14). Note how both the location and the number of equilibrium
points change for different values of the parameter r.
3.3 Linearisation around equilibrium points
The study of the behaviour