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A non-local PDE model for population dynamics with state-selective delay: local theory and global attractors. (English) Zbl 1082.92039
Summary: 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.

##### MSC:
 92D25 Population dynamics (general) 35B40 Asymptotic behavior of solutions to PDEs 37N25 Dynamical systems in biology 47N20 Applications of operator theory to differential and integral equations 47D03 Groups and semigroups of linear operators
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