Boolean Network, a Definition
A Boolean network is a system of n interconnected binary elements;
any element in the system can be connected to a series I of other
k elements, where k (and hence I) can vary. For each
individual element there is a logical or Boolean rule B which compute
its value based on the values of the elements connected with one. The state
of the system S is defined by the pattern of states (on/off or 0/1)
of all its elements. All elements are updated synchronously, moving the
system into its next state, and each state can has only one resultant state.
The total system space is defined as all possible N combinations
of the values of the n elements in S. The state of the system
is computed in discrete time steps. Therefore, at any moment (t) it is
defined as follows:
S(t+1)=f(S(t),{I1...
In}, {B1...Bn}).
Since the number of all possible states of the system is limited and the
transition rules are defined and do not depend on time, the system reaches
a cycle or attractor. It can be a steady state (point attractor) or a limit
cycle (dynamic attractor).
Attractors may be envisioned as the "target area" of the organism,
e.g. cell types at the end of development, repaired tissue following the
response to injury, or even the adaptation of metabolic gene expression
following a change in nutrient environment in microorganisms The limit
cycles in certain respects may reflect the biological rhythms.
All states leading to the same attractor constitute the basin of the attractor.
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