American Institute of Mathematical Sciences

Advanced
March  2008, 9(2): 249-266. doi: 10.3934/dcdsb.2008.9.249

Asymptotic behavior of size-structured populations via juvenile-adult interaction

József Z. Farkas 1, and  Thomas Hagen 2,

1. 

Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, United Kingdom
2. 

Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United States

Received  December 2006 Revised  October 2007 Published  December 2007

In this work a size-structured juvenile-adult population model is considered. The linearized dynamical behavior of stationary solutions is analyzed using semigroup and spectral methods. The regularity of the governing linear semigroup allows us to derive biologically meaningful conditions for the linear stability of stationary solutions. The main emphasis in this work is on juvenile-adult interaction and resulting consequences for the dynamics of the system. In addition, we investigate numerically the effect of a non-zero population inflow, due to an external source of newborns, on the linear dynamical behavior of the system in a special case of model ingredients.
Keywords: spectral analysis., linear stability, Structured population dynamics, juvenile-adult intraspecific interaction.
Mathematics Subject Classification: Primary: 92D25, 47D06; Secondary: 35B3.
Citation: József Z. Farkas, Thomas Hagen. Asymptotic behavior of size-structured populations via juvenile-adult interaction. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 249-266. doi: 10.3934/dcdsb.2008.9.249
[1]

Xianlong Fu, Dongmei Zhu. Stability analysis for a size-structured juvenile-adult population model. Discrete and Continuous Dynamical Systems - B, 2014, 19 (2) : 391-417. doi: 10.3934/dcdsb.2014.19.391
[2]

J. M. Cushing, Simon Maccracken Stump. Darwinian dynamics of a juvenile-adult model. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1017-1044. doi: 10.3934/mbe.2013.10.1017
[3]

Azmy S. Ackleh, Keng Deng. Stability of a delay equation arising from a juvenile-adult model. Mathematical Biosciences & Engineering, 2010, 7 (4) : 729-737. doi: 10.3934/mbe.2010.7.729
[4]

Azmy S. Ackleh, Keng Deng, Qihua Huang. Difference approximation for an amphibian juvenile-adult dispersal mode. Conference Publications, 2011, 2011 (Special) : 1-12. doi: 10.3934/proc.2011.2011.1
[5]

Tsuyoshi Kajiwara, Toru Sasaki. A note on the stability analysis of pathogen-immune interaction dynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 615-622. doi: 10.3934/dcdsb.2004.4.615
[6]

Rinaldo M. Colombo, Mauro Garavello. Stability and optimization in structured population models on graphs. Mathematical Biosciences & Engineering, 2015, 12 (2) : 311-335. doi: 10.3934/mbe.2015.12.311
[7]

G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 517-525. doi: 10.3934/dcdsb.2004.4.517
[8]

Robert Stephen Cantrell, Chris Cosner, Shigui Ruan. Intraspecific interference and consumer-resource dynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 527-546. doi: 10.3934/dcdsb.2004.4.527
[9]

Salvatore Rionero. A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal. Mathematical Biosciences & Engineering, 2006, 3 (1) : 189-204. doi: 10.3934/mbe.2006.3.189
[10]

Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633
[11]

Roberto Triggiani, Jing Zhang. Heat-viscoelastic plate interaction: Analyticity, spectral analysis, exponential decay. Evolution Equations and Control Theory, 2018, 7 (1) : 153-182. doi: 10.3934/eect.2018008
[12]

Yunfei Lv, Yongzhen Pei, Rong Yuan. On a non-linear size-structured population model. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3111-3133. doi: 10.3934/dcdsb.2020053
[13]

Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991
[14]

Xianlong Fu, Dongmei Zhu. Stability results for a size-structured population model with delayed birth process. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 109-131. doi: 10.3934/dcdsb.2013.18.109
[15]

Inom Mirzaev, David M. Bortz. A numerical framework for computing steady states of structured population models and their stability. Mathematical Biosciences & Engineering, 2017, 14 (4) : 933-952. doi: 10.3934/mbe.2017049
[16]

Hal L. Smith, Horst R. Thieme. Persistence and global stability for a class of discrete time structured population models. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4627-4646. doi: 10.3934/dcds.2013.33.4627
[17]

Shangzhi Li, Shangjiang Guo. Dynamics of a stage-structured population model with a state-dependent delay. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3523-3551. doi: 10.3934/dcdsb.2020071
[18]

Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1735-1757. doi: 10.3934/dcdsb.2015.20.1735
[19]

Jacques Henry. For which objective is birth process an optimal feedback in age structured population dynamics?. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 107-114. doi: 10.3934/dcdsb.2007.8.107
[20]

L. M. Abia, O. Angulo, J.C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1203-1222. doi: 10.3934/dcdsb.2004.4.1203

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (107)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy