The talk will give an overview of recent results for models of collective behavior governed by functional differential equations. It will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation), and engineering (swarm robotics), where latency (delay) plays a significant role. We will explain that there are two main sources of delay - inter-agent communications and information processing - and show that they have qualitatively different impacts on the group dynamics. We will give an overview of analytical methods for studying the asymptotic behavior of the models and their mean-field limits. Finally, motivated by situations where the finite speed of information propagation is significant, we will introduce an interesting class of problems where the delay depends nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
- 1999-2003 MSc. in Applied Mathematics, Charles U. in Prague
- 2003-2008 PhD. in Applied Mathematics, U. of Vienna
- 2008-2009 Postdoc in PDE Analysis, Vienna U. of Technology
- 2009-2012 Postdoc in PDE Analysis, Johann Radon Institute, Linz
- 2012-2020 Research Scientist, CEMSE, KAUST
- 2021-present Senior Research Scientist, CEMSE, KAUST