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Stability Analysis of Agent-Based Models

Undergraduate students:   Cassandra Cole (Brown University)
                                          Philip Doldo (Rensselaer Polytechnic Institute)
                                          Claire Qing Fan (Pomona College)
Grad student co-advisor:   Veronica Ciocanel
Advisor:                             Björn Sandstede

Agent-based models arise naturally in many different settings: pedestrians in a crowded room, shoaling fish, and cars on a road can all be studied as systems of moving agents. Often it is appropriate to consider a set number of agents (i.e. no off-ramp, constant number of cars), but some systems couple movement with random fluctuations in population size. This project was motivated by zebrafish, a small fish with black and yellow stripes that form due to the interactions of several types of pigment cells on the fish skin. The pigment cells interact by movement, birth, and death, and our previous agent-based model of zebrafish patterning suggests that the time-scales for migration and birth/death are similar. We are interested in understanding the stability of these stripes directly from an agent-based perspective, and, more generally, exploring the long-term behavior of general agent-based models that couple deterministic movement with random fluctuations in population size. Our work focuses first on a toy model of patterning in 1D and makes use of piecewise-deterministic Markov processes (PDMPs) to describe agent dynamics. Our goal is to prove the existence of a stationary distribution for the toy model and numerically solve the associated Fokker-Planck equation for this distribution.

Related (motivating) research: agent-based modeling of pattern formation on the body and fins of zebrafish

Alexandria Volkening - Last updated August 23, 2016