Recent studies in ecology and epidemiology indicate that it is important toinclude spatial heterogeneity, synchronization and seasonality in thetheoretical models. In this work, spatial heterogeneity is introduced viacoupled map lattices (CML) and partial differential equations. Stability andpersistence of some realistic CML are discussed. Chaos control, synchronizationand persistence are studied for some CML. Some applications in populationbiology and ecology are given. A simple method for finding the sufficientconditions for the existence of periodic solutions for differential equationswith periodic coefficients is given. This will simplify the study ofseasonality.
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