Uniform persistence and periodic solutions for some systems of delay differential equations

P. AMSTER

Workshop; International Workshop on Nonlinear Dynamical Systems and Functional Analysis; 2018

Simple criteria for persistence in some  systems of delay differential equations shall be presented. Inspired by a classical population model, we shall introduce sufficient conditions for weak or strong persistence and uniform persistence. As a consequence, we shall deduce the existence of positive periodic solutions. Moreover, we shall prove, in some cases, that the conditions are also necessary; in particular,  accurate assumptions will imply that 0 is a global attractor for all the positive solutions.