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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 9
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Original Articles

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

Jozsef Z. Farkas Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UKCorrespondence[email protected]
&
Thomas Hagen Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA
Pages 1087-1103 | Received 22 Mar 2007, Accepted 25 Jul 2007, Published online: 04 Oct 2007

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Rong Liu & Guirong Liu. (2020) Optimal contraception control for a size-structured population model with extra mortality. Applicable Analysis 99:4, pages 658-671.
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Articles from other publishers (21)

Zhuxin Ni & Qihua Huang. (2024) A nonautonomous model for the interaction between a size-structured consumer and an unstructured resource. Journal of Mathematical Biology 88:5.
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Dongdong Ni, Wanbiao Ma & Malay Banerjee. (2023) Dynamics of a PDE model with size-structure: Characterizing the growth and flocculation effects of unicellular algae. Chaos, Solitons & Fractals 167, pages 113054.
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Wei Gong & Zhanping Wang. (2023) Stability of nonlinear population systems with individual scale and migration. AIMS Mathematics 8:1, pages 125-147.
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Dandan Hu & Gang Huang. (2022) Dynamical analysis on a size-structured population model of Daphnia with delayed birth process. Chaos, Solitons & Fractals 161, pages 112367.
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Carles Barril, Àngel Calsina, Odo Diekmann & József Z. Farkas. (2022) On the formulation of size-structured consumer resource models (with special attention for the principle of linearized stability). Mathematical Models and Methods in Applied Sciences 32:06, pages 1141-1191.
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Rong Liu & Guirong Liu. (2020) Theory of optimal harvesting for a size structured model of fish. Mathematical Modelling of Natural Phenomena 15, pages 1.
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Simran K. Sandhu, Andrew Yu. Morozov & József Z. Farkas. (2019) Modelling evolution of virulence in populations with a distributed parasite load. Journal of Mathematical Biology 80:1-2, pages 111-141.
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József Z. Farkas. (2018) Net reproduction functions for nonlinear structured population models. Mathematical Modelling of Natural Phenomena 13:3, pages 32.
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Erica M. Rutter, H. T. Banks, Gerald A. LeBlanc & Kevin B. Flores. (2017) Continuous Structured Population Models for Daphnia magna. Bulletin of Mathematical Biology 79:11, pages 2627-2648.
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Àngel Calsina, Odo Diekmann & József Z. Farkas. (2016) Structured populations with distributed recruitment: from PDE to delay formulation. Mathematical Methods in the Applied Sciences 39:18, pages 5175-5191.
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Dongxue Yan, Yu Cao & Xianlong Fu. (2016) Asymptotic analysis of a size-structured cannibalism population model with delayed birth process. Discrete and Continuous Dynamical Systems - Series B 21:6, pages 1975-1998.
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J. Z. Farkas, A. Yu. Morozov, E. G. Arashkevich & A. Nikishina. (2015) Revisiting the Stability of Spatially Heterogeneous Predator–Prey Systems Under Eutrophication. Bulletin of Mathematical Biology 77:10, pages 1886-1908.
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Lai Zhang, Michael Pedersen & Zhigui Lin. (2015) Stability patterns for a size-structured population model and its stage-structured counterpart. Mathematical Biosciences 267, pages 109-123.
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Kaska Adoteye, H.T. Banks, Karissa Cross, Stephanie Eytcheson, Kevin B. Flores, Gerald A. LeBlanc, Timothy Nguyen, Chelsea Ross, Emmaline Smith, Michael Stemkovski & Sarah Stokely. (2015) Statistical validation of structured population models for Daphnia magna. Mathematical Biosciences 266, pages 73-84.
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Xianlong Fu & Dongmei Zhu. (2014) Stability analysis for a size-structured juvenile-adult population model. Discrete & Continuous Dynamical Systems - B 19:2, pages 391-417.
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Àngel Calsina & József Z. Farkas. (2014) Positive Steady States of Evolution Equations with Finite Dimensional Nonlinearities. SIAM Journal on Mathematical Analysis 46:2, pages 1406-1426.
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J. Z. Farkas & A. Y. Morozov. (2014) Modelling Effects of Rapid Evolution on Persistence and Stability in Structured Predator-Prey Systems. Mathematical Modelling of Natural Phenomena 9:3, pages 26-46.
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Xianlong Fu & Dongmei Zhu. (2013) Stability results for a size-structured population model with delayed birth process. Discrete & Continuous Dynamical Systems - B 18:1, pages 109-131.
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M. El-Doma. (2012) A size-structured population dynamics model of Daphnia. Applied Mathematics Letters 25:7, pages 1041-1044.
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József Z. Farkas. (2010) Size-structured populations: immigration, (bi)stability and the net growth rate. Journal of Applied Mathematics and Computing 35:1-2, pages 617-633.
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Yan Liu & Ze-Rong He. (2009) Stability results for a size-structured population model with resources-dependence and inflow. Journal of Mathematical Analysis and Applications 360:2, pages 665-675.
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