Large population limit of interacting population dynamics via generalized gradient structures
Abstract
This chapter focuses on the derivation of a doubly nonlocal FisherKPP model, which is a macroscopic nonlocal evolution equation describing population dynamics in the large population limit. The derivation starts from a microscopic individualbased model described as a stochastic process on the space of atomic measures with jump rates that satisfy detailed balance w.r.t. to a reference measure. We make use of the socalled `cosh' generalized gradient structure for the law of the process to pass to the large population limit using evolutionary Gammaconvergence. In addition to characterizing the large population limit as the solution of the nonlocal FisherKPP model, our variational approach further provides a generalized gradient flow structure for the limit equation as well as an entropic propagation of chaos result.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.05894
 arXiv:
 arXiv:2406.05894
 Bibcode:
 2024arXiv240605894H
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Probability
 EPrint:
 Contributed chapter to the book "Active Particles" (Volume 4)