Periodicity induced partial synchronization

J.C.M. Swarts, H. Nijmeijer (Supervisor), M. Silva Baptista, da (Supervisor)

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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 singularly. 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.
Original languageEnglish
Place of PublicationEindhoven
PublisherEindhoven University of Technology
Publication statusPublished - 2011

Publication series


Bibliographical note

Traineeship report. - DC 2011.073


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