Alladi Ramakrishnan Hall

Cluster synchronization in networks

Aradhana Singh

IMSc Chennai

The interaction between individual units of a system leads to many emerging behaviors, among which synchronization is one of a fascinating phenomenon, which has been gaining tremendous attention since the first experimental demonstration of the phenomena by Huygens. Synchronization is defined as an emergence of some relation between the functional of two processes due to interaction. Our thoughts, action, motion, perceptions all are controlled by the synchronization of neurons in the brain. Additionally, synchronization plays very important role in electric power systems, digital audio, video, inscription in telecommunication, metabolic systems etc and has motivated an intense research in these systems. Synchronization can be global as well as local. The local synchronization leads to the cluster formation which is desired in some cases such as in the neural networks and undesired in some cases such as power grid networks and thus has drawn tremendous attention in the last decade. Moreover, the finite speed of information transmission leads to time delay, which plays a vital role in synchronization. Further, the real-world networks such as networks of transport, power grids, banks, genes, neurons, cells, stock market consist of multiple levels of interactions. Therefore, the functioning of individuals in one layer gets also affected by interactions from other layers, called multiplexing. I will focus on the interplay between the underlying network structure and dynamical clusters of the isolated as well as the multiplex networks and will discuss the impact of communication delay on cluster synchronizability and cluster patterns.