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

By A. Rezounenko, Jianhong Wu. 2006

109 citations recorded by the source corpus.

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.

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/64e256e61bc9ae91f9a8f2d385e582e4fa09db01

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Tibor Krisztin
2. A. Rezounenko

In Public Health, Environmental and Occupational Health

1. Tibor Krisztin
2. A. Rezounenko
3. E. Hernández
4. Rathinasamy Sakthivel
5. Ferenc Hartung

In Sociology and Political Science

1. Tibor Krisztin
2. A. Rezounenko

Citations in the corpus

• Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold (2014, methodology): “In the present work we rely on the study of solution manifold for ODEs [12, 14, 25] The study of PDEs with state-dependent delay are naturally more difficult and was initiated only recently [17, 18, 19, 20, 21, 22].”
• Existence results for impulsive evolution differential equations with state-dependent delay. (2008, background): “There exists a extensive literature for ordinary state-dependent delay equations, see among another works, [2, 1, 3, 4, 6, 7, 8]. The study of partial dierential equations with state dependent delay have been initiated recently, and concerning this matter we cite the pioneer works Rezounenko et al. ”
• Existence results for an impulsive neutral functional differential equation with state-dependent delay (2007, background): “The literature related to partial functional differential equations with state dependent delay is very recent and limited, to our knowledge, to the works 3 , 20–22 , 33 .”