SIAM Journal on Applied Mathematics
Analysis of a model representing stage-structured population growth with state-dependent time delay
SIAM Journal on Applied Mathematics
Slowly oscillating periodic solutions of autonomous state-dependent delay equations
Nonlinear Analysis: Theory, Methods & Applications
Inertial manifolds for retarded semilinear parabolic equations
Nonlinear Analysis: Theory, Methods & Applications
Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation
Applied Mathematics and Computation
Dynamics of projective adaptive resonance theory model: the foundation of PART algorithm
IEEE Transactions on Neural Networks
Existence results for an impulsive abstract partial differential equation with state-dependent delay
Computers & Mathematics with Applications
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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.