Information Technology Reference
In-Depth Information
In the previous subsections, we proposed a dyad of agent which mutually influence.
If we replace the non-verbal behaviours of agents by their internal states in the system
of equations 5, it gives:
S
1
(
t
+1)=
S
1
(
t
)+
u
1
V
Act
1
(
t
+1)+
σth
β
(
S
2
(
t
))
S
2
(
t
+1)=
S
2
(
t
)+
u
2
V
Act
1
(
t
+1)+
σth
β
(
S
1
(
t
))
(6)
To enable coupling to occur, the agents should also be dynamical systems: systems
which state evolves along time by themselves. The internal state of the agents
S
i
pro-
duces behaviours and is influenced by the other agent's behaviour. To ensure internal
dynamics, we made this internal state a relaxation oscillator, which increases linearly
and decreases rapidly when it reaches the threshold
0
.
95
(Fig.5 shows an example of
the signals obtained). By oscillating , the internal states agents will not only influence
each other but also be able to correlate one with the other [23].
Here, two cases are interesting.
When the internal states of both agents are under the threshold triggering non-verbal
behaviours,
β
, the system of equation 6 becomes:
S
1
(
t
+1)=
S
1
(
t
)+
u
1
V
Act
1
(
t
+1)
S
2
(
t
+1)=
S
2
(
t
)+
u
2
V
Act
1
(
t
+1)
(7)
The two agents are almost independent, they are only influenced by the speech of
Agent1 and each one produces its own oscillating dynamic. That could be the case
if two tired people (high
β
) speak about a not so interesting subject (
u
i
are low): they
are made apathic by the conversation, they do not express anything.
The second interesting case is when both agents' internal states are above the thresh-
old
β
. The system of equation 6 becomes:
S
1
(
t
+1)=
S
1
(
t
)+
u
1
V
Act
1
(
t
+1)+
σS
2
(
t
)
S
2
(
t
+1)=
S
2
(
t
)+
u
2
V
Act
1
(
t
+1)+
σS
1
(
t
)
(8)
In this case agents are not anymore independent, they influence each other depending
on the way they understand speech. If we push the recursivity of these equations one
step further we obtain:
S
1
(
t
+1)=
S
1
(
t
)+
u
1
V
Act
1
(
t
+1)+
σ
(
S
2
(
t −
1) +
u
2
V
Act
1
(
t
)+
σS
1
(
t −
1))
S
2
(
t
+1)=
S
2
(
t
)+
u
1
V
Act
1
(
t
+1)+
σ
(
S
1
(
t −
1) +
u
1
V
Act
1
(
t
)+
σS
2
(
t −
1))
(9)
And now we see the effect of coupling, that is to say that agents are not only influenced
by the state of the other but they are influenced by their own state, mediated by the other:
the non-verbal behaviours of the other becomes their own biofeedback [17]. When the
threshold
β
is overtaken, the reciprocal influence is recursive and becomes exponential:
the dynamics of
S
1
and
S
2
are not any more independent, they are influenced in their
phases and frequencies [21,23].
3
Test of the Model
We tested this model by implementing a dyad of agent as a neuronal network in the
neuronal network simulator Leto/Prometheus (developed in the ETIS lab. by Gaussier
et al. [9,10]), and by studying its emerging dynamics with different sets of parameters.
