  Recent studies in ecology and epidemiology indicate that it is important to
include spatial heterogeneity, synchronization and seasonality in the
theoretical models. In this work, spatial heterogeneity is introduced via
coupled map lattices (CML) and partial differential equations. Stability and
persistence of some realistic CML are discussed. Chaos control, synchronization
and persistence are studied for some CML. Some applications in population
biology and ecology are given. A simple method for finding the sufficient
conditions for the existence of periodic solutions for differential equations
with periodic coefficients is given. This will simplify the study of
seasonality.
