This project will study various classes of differential equations which generate dynamical systems with some monotonicity properties which limit the complexity of their asymptotic behavior. Included are certain classes of ordinary differential equations, delay differential equations and reaction-diffusion systems with time delays. The goal of the research is to describe global qualitative features of the flow. For finite dimensional systems we focus on existence and nonexistence of nontrivial periodic orbits and associated invariant manifolds. For infinite dimensional systems, the principal investigator will focus on convergence of solutions to equilibrium, invariance and comparison type results. Systems of the type considered here occur frequently in the applied literature and particularly in mathematical models in biology. Results with significant applications are expected.
