Dynamics on Complex Networks
The world is more connected than ever! There is a tendency towards collective motion in nature such as
.:: heart: pacemaker cells must be in synchrony to create a proper heartbeat
.:: bird flocks, fish schools: for protection from danger, finding food, to survive
.:: power grids: too much money invested for energy by countries, the grid has to be in sync
and many more, hand clapping in a theatre, neural activity...
And many of those dynamical systems have chaotic behavior, that's why the prediction is impossible. But how come such chaotic systems oscillate in unison. I am deeply interested in the emergence of "Collective Behavior of Chaotic Units on Complex Networks".
Time Series Analysis
Unrevealing the nature from observations! In order to understand the dynamical behavior of systems in a broad range of scientific fields such as physics, biology, medicine, climatology, economy, etc., time series analysis provides crucial techniques.
I am mainly interested in reconstructing phase space of these systems from observations and understand underlying dynamics using the Poincaré recurrences. Recurrence Plot and Networks are powerful tools that use the Poincaré recurrences theorem.