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Synthetic Gene Network
book

Synthetic Gene Network

by Bor-Sen Chen, Yu-Chao Wang
May 2014
Intermediate to advanced content levelIntermediate to advanced
216 pages
6h 47m
English
CRC Press
Content preview from Synthetic Gene Network
()
()
()
1
1
11 1
1
Co , , ,
∂+
⎛⎞
⎜⎟
⎜⎟
⎛⎞
⎛⎞⎛
⎜⎟
∂+
⎜⎟
⎜⎟⎜
⎜⎟
⎜⎟
⎜⎟⎜
∈∀
⎜⎟
⎜⎟
⎜⎟⎜
⎜⎟
⎜⎟
⎜⎟⎜
⎜⎟
⎜⎟
⎝⎠⎝
⎝⎠
∂+
⎜⎟
⎜⎟
⎝⎠

d
M
d
M
mmM
md
fx x
x
FF
gxx
GG
x
x
GG
gxx
x
(3.10)
where Co denotes the convex hull of polytope with M vertices defi ned in
(3.10), then the state trajectories x
~
(t) of the shifted gene network in (3.1) will
belong to the convex combination of the state trajectories of the following
M linearized synthetic gene networks derived from the vertices of the
polytope in (3.10) (Boyd et al. 1994, Chen and Wu 2009)
()
1
, 1, ,
=
=++ =

m
jiiji
i
dx NF x v dt M G xdW E j M
(3.11)
By the global linearization theory (Boyd et al. 1994), if (3.10) holds,
then every trajectory ...
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Publisher Resources

ISBN: 9781466592698