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Abstract

The objective of these lectures is to apply the theory of linear and nonlinear semigroups of operators to models of structured populations dynamics. The mathematical models of structured populations are typically partial differential equations with variables corresponding to such properties of individual as age, size, maturity, proliferative state, quiescent state, phenotype expression, or other physical properties. The main goal is to connect behavior at the individual level to behavior at the population level. Theoretical results from semigroup theory are applied to analyze such population behaviors as extinction, growth, stabilization, oscillation, and chaos.