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