Cyber-Physical Systems

Hybrid Stochastic Synchronization and Flow Models 125

vector g

i

[k] is simply



g

i1

··· g

in



T

. We note that this stochastic synchronization network model is

actually a mixture of a voting model and a distributed averaging model. We note that the instantiation

matrix G[k] (i.e., G[k] =



g

1

[k] ··· g

n

[k]



) depends on the current opinions of the agents.

Although the two synchronization mechanisms in the two operating regimes (i.e., above threshold

and below threshold) are completely different, the model is stochastically linear. Let us use notation

¯

G[k] where the i, jth entry of

¯

G[k] has value g

ji

. For the case that s

i

[k]≥b

i

(voting model phase), we

can easily obtain that E(s[k +1]|s[k]) =

¯

G

T

[k]s[k]. For the case that s

i

[k] < b

i

for any i (distributed

averaging ...