welcome to all work on guaranteed global synchronisation networks were stochastic interaction
synchronization is that it in various view that shared by all the two
you think
and engineering
right on the one inside you might have
continuous coupling
you might have on the other hand side this continuous part company
especially in the field of wireless communication
where packets are transmitted
and receive
quite naturally a discontinuous system
so you're interested in parts coupling
at the strategy to
achieve synchronization
with that just to them
you might have
i which are net the conditions
and individual delay and additionally you will have a probability to read the packet
this mean
that
there is a chance
then the signal that is transmitted is not going to be written
the that's all the to be taken into account
if you want to achieve and guarantee think annotation
and that's exactly what we do
and i'm going to show you now how we going to achieve this goal
let us take
late the running
on a circle
here's the all clear
entrance counterclockwise on the circle until it passes the threshold
whenever tested a threshold
it will emitted signal
with some probability
p ten
any oscillator
on the circle which receives the signal
that's a here's austria that k
years austria later j
so whenever one of those received signal emitted by oscillator
i
it will adjust
it will adjust according to our update function
this means basically that are not later that is in the lower ha
will jump
for words
and then also later that is in the above
will jump backwards
that the main idea of the update function is to oscillators
one the d m at their
of the set
the i
and we will not know that is the i
we monotonically decreases
for combination of how this applies to bigger is that of oscillators
will not be shown in the video
on the left we see realization with ten oscillators on the random network
if i of an oscillator is indicated by red light
on the top right we show the oscillator spaces at the five times
note that the y-axis is centered around zero
well oscillators between the plot lines are combined in a set s
on the bottom right with you did em at their of this and the size
of face
as soon as well oscillators are you know s then d s equals d i
and is monotonically decreasing and synchronization is achieved
after all this technical detail
we are now able to see the bigger picture
we guaranteed synchronisation
for arbitrary network conditions
for arbitrary individual the late
and sarcastic interactions
did not give the guarantee
and that and out that to better include those things for applications
such as they may connect works
robert swarming
and network protocols for wireless communications
thank you