Linear stability and positivity results for a generalized size-structured Daphnia model with inflow§

Citation

Farkas JZ & Hagen T (2007) Linear stability and positivity results for a generalized size-structured Daphnia model with inflow§. Applicable Analysis, 86 (9), pp. 1087-1103. http://www.informaworld.com/smpp/content~db=all~content=a782010393; https://doi.org/10.1080/00036810701545634

Abstract
We employ semigroup and spectral methods to analyze the linear stability of positive stationary solutions of a generalized size-structured Daphnia model. Using the regularity properties of the governing semigroup, we are able to formulate a general stability condition which permits an intuitively clear interpretation in a special case of model ingredients. Moreover, we derive a comprehensive instability criterion that reduces to an elegant instability condition for the classical Daphnia population model in terms of the inherent net reproduction rate of Daphnia individuals.

Keywords
Predator-prey interaction; structured population dynamics; semigroup methods; Daphnia; Daphnia; Population dynamics

Journal
Applicable Analysis: Volume 86, Issue 9