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Feedback Control in Systems Biology
book

Feedback Control in Systems Biology

by Carlo Cosentino, Declan Bates
October 2011
Intermediate to advanced content levelIntermediate to advanced
296 pages
9h 39m
English
CRC Press
Content preview from Feedback Control in Systems Biology
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 ...
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Publisher Resources

ISBN: 9781439816912