Persistence of globally attractive periodic solutions under discretization in Hammerstein equations
Summary
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.