Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study

Hal Smith

doi:10.1016/0025-5564(93)90006-V

Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study

Hal Smith

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

59 Scopus citations

Abstract

It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability.

Original language	English (US)
Pages (from-to)	1-23
Number of pages	23
Journal	Mathematical Biosciences
Volume	113
Issue number	1
DOIs	https://doi.org/10.1016/0025-5564(93)90006-V
State	Published - Jan 1993

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

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10.1016/0025-5564(93)90006-V

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title = "Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study",

abstract = "It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability.",

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AB - It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability.

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Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study

Abstract

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