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SUMMARY:Non-Markovian models of collective motion - Jan Haskovec (King Abd
 ullah University of Science and Technology (KAUST))
DTSTART:20231110T113000Z
DTEND:20231110T123000Z
UID:TALK203242@talks.cam.ac.uk
DESCRIPTION:I will give an overview of recent results for models of collec
 tive behavior governed by functional differential equations with non-Marko
 vian structure. The talk will focus on models of interacting agents with a
 pplications in biology (flocking\, swarming)\, social sciences (opinion fo
 rmation) and engineering (swarm robotics)\, where latency (delay) plays a 
 significant role. I will characterize two main sources of delay - inter-ag
 ent communications ("transmission delay") and information processing ("rea
 ction delay") - &nbsp\;and discuss their impacts on the group dynamics. I 
 will give an ovierview of analytical methods for studying the asymptotic b
 ehavior of the models in question and their mean-field limits. In particul
 ar\, I will show that the transmission vs. reaction delay leads to fundame
 ntally different mathematical structures and requires appropriate choice o
 f analytical tools. Finally\, motivated by situations where finite speed o
 f information propagation is significant\, I 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 an
 d open problems here.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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