Biology Reference
In-Depth Information
FIGURE 6.3
State transition digraph for the network
N
D
,1,1
=
with connectivity
D
as in Fig-
ure
6.2
(b). Adapted from [
5
].
attraction of the remaining four attractors aremuch larger and contain several transient
states each. Possible transients show up as directed paths outside of the union of the
attractors that end in a state that is succeeded by a state in the attractor. For example,
{(34567), (12), (4567), (23)} and {(12), (4567), (23)} are transients for the trajectories
with initial states coded by (34567) and (12), respectively, but {(34567), (12), (4567)}
cannot be the transient of any trajectory.
Exercise 6.4.
What is the maximum length of a transient for the system of
Figure
6.3
? List all
initial states for which transients have this maximum
length.
Exercise 6.5.
a.
Draw the state transition digraph for the neuronal network
N
of Example
6.3
.
Hint:
The network has 24 distinct states.
b.
Find all attractors, their lengths, and the sizes of the basins of attraction for the
neuronal network
N
of Example
6.3
.
c.
What is the maximum length of a transient in this network?
All our networks have exactly one steady state attractor. When does a network also
have other periodic attractors?We have seen that such attractors correspond to directed
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