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Intra-specific competition and insect larval development: a model with time-dependent delay

Part of: Functional-differential and differential-difference equations

Published online by Cambridge University Press:  30 January 2017

Stephen A. Gourley ,
Rongsong Liu  and
Yijun Lou
Stephen A. Gourley
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK (s.gourley@surrey.ac.uk)
Rongsong Liu
Affiliation:
Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA
Yijun Lou
Affiliation:
Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
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Extract

We derive a stage-structured model for an insect population in which a larva matures on reaching a certain size, and in which there is intra-specific competition among larvae that hinders their development, thereby prolonging the larval phase. The model, a system of delay differential equations for the total numbers of adults and larvae, assumes two forms. One of these is a system with a variable state-dependent time delay determined by a threshold condition, the other has constant and distributed delays, a size-like independent variable replacing time t, and no threshold condition. We prove theorems on boundedness and on the linear stability of equilibria.

Keywords

competitiondelaysize-structurestabilityboundedness

MSC classification

Secondary: 34K12: Growth, boundedness, comparison of solutions 34K20: Stability theory 92D40: Ecology
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 2 , April 2017 , pp. 353 - 369
Copyright
Copyright © Royal Society of Edinburgh 2017 

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