
82 Feedback Control in Systems Biology
0
0.1
0.2
0.3
0.4
0.5
0
1
2
3
4
−6
−4
−2
0
2
x
1
x
2
FIGURE 3.8: Surface described by the derivative of the Lyapunov function
in Exa mple 3.5.
cellular or population level. First of all let us give a more precise definition
of region of attractio n.
Region of Attraction: Let the origin x = 0 be an asymptotically
stable equilibrium point for the nonlinear system (3.8) and let Φ(t, x
0
)
be the solution of Eq. (3.8) that starts at initial state x
0
at time t = 0.
The region of attraction of t he origin, denoted by R
A
, is defined by
R
A
= {x
0
: Φ(t, x
0
) → 0 as t → ∞}.
A no table property of the region of attraction is that the boundary of R
A
is ...