Large population limit of interacting population dynamics via generalized gradient structures
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917689181601792 |
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| author | Hoeksema, Jasper Hraivoronska, Anastasiia Tse, Oliver |
| author_facet | Hoeksema, Jasper Hraivoronska, Anastasiia Tse, Oliver |
| contents | This chapter focuses on the derivation of a doubly nonlocal Fisher-KPP model, which is a macroscopic nonlocal evolution equation describing population dynamics in the large population limit. The derivation starts from a microscopic individual-based 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 so-called `cosh' generalized gradient structure for the law of the process to pass to the large population limit using evolutionary Gamma-convergence. In addition to characterizing the large population limit as the solution of the nonlocal Fisher-KPP model, our variational approach further provides a generalized gradient flow structure for the limit equation as well as an entropic propagation of chaos result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large population limit of interacting population dynamics via generalized gradient structures Hoeksema, Jasper Hraivoronska, Anastasiia Tse, Oliver Analysis of PDEs Probability This chapter focuses on the derivation of a doubly nonlocal Fisher-KPP model, which is a macroscopic nonlocal evolution equation describing population dynamics in the large population limit. The derivation starts from a microscopic individual-based 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 so-called `cosh' generalized gradient structure for the law of the process to pass to the large population limit using evolutionary Gamma-convergence. In addition to characterizing the large population limit as the solution of the nonlocal Fisher-KPP model, our variational approach further provides a generalized gradient flow structure for the limit equation as well as an entropic propagation of chaos result. |
| title | Large population limit of interacting population dynamics via generalized gradient structures |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2406.05894 |