Emergence of controlled dynamics and role of topology in complex networks

Abstract

The complexity of several systems is a confluence of the intricate structure of their interactions and the intrinsic dynamics of its constituent elements. Complex network framework can be used to study such systems effectively. Several recent studies indicate that understanding of the complex systems may be better achieved by using both the nodal dynamics and the interaction topology synergetically to alter the behaviour of the system.

We discuss properties of individual nonlinear systems and the dynamics displayed in collective behaviour including synchronization, phase-synchronization, amplitude and oscillation deaths, chimera state behaviour etc. We explore the emergent dynamics especially synchronization, by investigating control strategies where: i) strategic rewiring brings system toward desired synchronization dynamics and ii) the system dynamics drives changes in the interaction topology leading to an emergent stable network structure.

We observe the formation of synchronization in clusters where the clusters either remain or coalesce into larger clusters. We are also able to change the number of clusters by varying control parameters. For dynamics driven control of topology, we observe resultant networks showing characteristics of scalefree type networks. Finally, we identify possible improvements to control procedures studied and propose a method involving externally driven control to extend the study further.