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职业迁徙
个人简介
My core personal research focuses on applications of mathematics to biology and ecology. In particular, I am interested in linking animal behavior, population dynamics and evolutionary processes. My goal is to create mathematical models that allow for a better understandig of key mechanisms that preserve biodiversity on Earth. To this end I combine game theoretical methods with differential equations. In particular, I employ separation of time scales by assuming that behavioral processes operate on a much faster time scale when compared to population dynamics. This approach is complementary to the adaptive dynamics approach that assumes population dynamics operate on much faster time scale than evolution of traits. The approach I have developed is based on the assumption that behavioral traits, often described as an evolutionarily stable strategy of a game instantaneously track population densities. This assumption in some cases leads to a feedback map between population densities and trait values that is multi-valued. Substituting this feedback map to population dynamics in such cases results in a differential inclusion, or a multi-valued differential equation. For low dimensional systems, these resulting models are often at least partially analyzable.
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crossref(2024)
DYNAMIC GAMES AND APPLICATIONSno. 4 (2023): 1049-1065
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