Slides for the Ignite talk at European Conference on Complex Systems (ECCS '14). Lucca, Italia, September 2014

1. Generalization of consensus processes
in dynamic networks
M. Rebollo, J.C. Losada, J. Galeano, R.M. Benito
Univ. Politècnica de València, Univ. Politécnica de Madrid
Ruled by
converges to
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0 2 4 6 8 10
time
x
Consensus process
x
1
x
2
x
3
x
4
xt+1
i = xti
+ "
X
j2Nt
i
⇥
xt
j xti
⇤
lim
t!1
xi =
P
i x0i
N

2. key concept:
sum conservation
s =
X
i
x0i
=
X
i
xti
8t
values can be
corrected locally
t+1
i = min
j2Nt
i [i
t
j
xt+1
i = xti
+ f(xti
) +
ti
wt
i
X
j2Nt
i
⇥
xt
j xti
⇤
+ ti
local corrections adaption to dynamic ℇ

3. 0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0 2 4 6 8 10
time
x
Consensus process
0.5
0.45
0.4
0.35
0.3
Consensus with changes in initial values
x
0.25
0.2
0.15
0.1
time 0 5 10 15
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0 2 4 6 8 10
time
x
Consensus process with node deletion
0 5 10 15
time
x
Consensus with changes in weights
Adapts to
changes in
• initial values
• weights
• network structure
• learning parameter