Dynamical Systems and Population Persistence

摘要: The mathematical theory of persistence answers questions such as which species, in a model interacting will survive over the long term. It applies to infinite-dimensional well finite-dimensional dynamical systems, and discrete-time continuous-time semiflows. This monograph provides self-contained treatment that is accessible graduate students. key results for deterministic autonomous systems are proved full detail acyclicity theorem tripartition global compact attractor. Suitable conditions given imply strong even nonautonomous semiflows, time-heterogeneous developed using so-called ""average Lyapunov functions"". Applications play large role from beginning. These include ODE models an SEIRS infectious disease meta-population nonlinear matrix demographic dynamics. Entire chapters devoted examples including SI epidemic with variable infectivity, microbial growth tubular bioreactor, age-structured cells growing chemostat.