The field of synchronization in networks of oscillators has received great attention lately. Theory
has shown that it is hard to achieve complete synchronization in large scale networks, even when
all the nodes have equal dynamics. This work will show that partial synchronization has milder
conditions and should be expected to be found more commonly in nature. There is already plenty
of research in partial synchronization of networks, most of it is based on symmetries of the system.
Unfortunately, these works only demonstrate the appearance of partial synchronization for
networks with symmetry.
Even without symmetry, the nodes in a network can be synchronized partially in a very special
way, that we call periodically induced synchronization. For this phenomenon to appear the most
important parameters are the number of connections of a node and the couplings strength. The
remarkable result of our theory is that each node can become partially synchronous to other nodes
if we tune these parameters appropriately. The calculation when a node becomes partially synchronous to other nodes can be done without the need of any elaborate mathematical algebra as
for example the diagonalization of the network. With this exciting result every node is controlled
This phenomenon is characterized by nodes with similar degree that act in a similar way, it is a
general phenomena to be expected to be found in large scale networks. Periodic induced synchronization can be used to analyze large networks.
A possible field where our theory applies to is for example biology, the synchronization of a network
of neuron cells. Where some cells are highly connected while others are less connected.
Such cases are typically present in our brain as well as in our nerve system. Also in social networks
this theory can give insights in the social behavior of groups. This opens up the analysis of
the network of people, where some people have many friends, and others have few.
Traineeship report. - DC 2011.073