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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
260 Feedback Control in Systems Biology
8.3.1 The effective stability approximation
The basic idea of this approach is as follows. Consider a system of biomolec-
ular interactions represented by the nonlinear differential equation
dx(t)
dt
= f[x(t)] (8.3)
where x R
n
, f[x(t)] satisfies the standard conditions for the existence and
uniqueness of the solution of the differential equation, R is the real number
field and n is a positive integer. Linea r stability analysis of such equations
is performed around the equilibrium point, x
s
, which satisfies f(x
s
) = 0, as
follows:
dx(t)
dt
=
∂f(x)
∂x
x=x
s
x(t) Γ∆x(t) (8.4)
where we assume that all real par ts of the
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Publisher Resources

ISBN: 9781439816912