
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:
d∆x(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