A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors

We propose a non-local PDE model for the evolution of a single species population that involves delayed feedback, where the delay such as the maturation time in the delayed birth rate, is selective and the selection depends on the status of the system. This delay selection, in contrast with the usual state-dependent delay widely used in ordinary delay differential equation, ensures the Lipschitz continuity of the nonlinear functional in the classical phase space. We also develop the local theory, and the existence and upper semi-continuity of the global attractor with respect to parameters.