Robust uniform persistence for structured models of delay differential equations

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<p style='text-indent:20px;'>We consider a general class of delay differential equations systems, typically used to model the dynamics of structured biological populations, and establish necessary conditions for the part of the attractor contained in the boundary of the state space to repel the complementary dynamics contained in the interior of the state space. The conditions are formulated in terms of Lyapunov exponents and invariant probability measures and we use them to prove a robust uniform persistence result.</p>