Persistence of globally attractive periodic solutions under discretization in Hammerstein equations

Abstract

Hammerstein equations are a type of integrodifference equations (IDEs), which are a type of discrete-time dynamical systems defined on a state space of functions. They have a wide variety of practical applications, such as modeling growth and dispersal of populations. For simulation purposes, appropriate discretization methods need to be applied on IDEs. However, it is still an open question to what extend the dynamics of a discretized IDE resemble the dynamics of the original system. Recently, the first results adressing this question have been published. This thesis elaborates on the discretization methods that can be applied to IDEs, as well as on results of the recent publication, with an emphasis on Hammerstein IDEs.