711
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Persistence and global stability in a selection–mutation size-structured model

, &
Pages 436-453 | Received 26 Mar 2010, Accepted 03 Nov 2010, Published online: 14 Apr 2011

References

  • Ackleh , A. S. and Deng , K. 2004 . Survival of the fittest in a quasilinear size-structured population model . Natur. Resource Modeling , 17 : 213 – 228 .
  • Ackleh , A. S. and Hu , S. 2007 . Comparison between stochastic and deterministic selection–mutation models . Math. Biosci. Eng. , 4 : 133 – 157 .
  • Ackleh , A. S. and Ito , K. 1997 . An implicit finite difference scheme for the nonlinear size-structured population model . Numer. Funct. Anal. Optim. , 18 : 865 – 884 .
  • Ackleh , A. S. , Banks , H. T. and Keng Deng . 2002 . A finite difference approximation for a coupled system of nonlinear size-structured populations . Nonlinear Anal. , 50 : 727 – 748 .
  • Ackleh , A. S. , Deng , K. and Wang , X. 2004 . Competitive exclusion and coexistence for a quasilinear size-structured population model . Math. Biosci. , 192 : 177 – 192 .
  • Ackleh , A. S. , Banks , H. T. , Deng , K. and Hu , S. 2005 . Parameter estimation in a coupled system of nonlinear size-structured populations . Math. Biosci. Eng. , 2 : 289 – 315 .
  • Ackleh , A. S. , Deng , K. and Huang , Q. 2010 . Existence-uniqueness results and difference approximations for an amphibian juvenile-adult model . Contemp. Math. , 513 : 1 – 23 .
  • Calsina , À. and Cuadrado , S. 2004 . Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics . J. Math. Biol. , 48 : 135 – 159 .
  • Calsina , À. and Cuadrado , S. 2005 . Stationary solutions of a selection mutation model: The pure mutation case . Math. Models Methods Appl. Sci. , 15 : 1091 – 1117 .
  • Calsina , À. and Cuadrado , S. 2007 . Asymptotic stability of equilibria of selection–mutation equations . J. Math. Biol. , 54 : 489 – 511 .
  • Calsina , À and Saldaña , J. 1995 . A model of physiologically structured population dynamics with a nonlinear individual growth rate . J. Math. Biol. , 33 : 335 – 364 .
  • Cuadrado , S. 2009 . Stability of equilibria of a predator–prey model of phenotype evolution . Math. Biosci. Eng. , 6 : 701 – 718 .
  • Cushing , J. M. 1990 . Some competition models for size-structured populations . Rocky Mountain J. Math. , 20 : 879 – 897 .
  • Cushing , J. M. 1998 . An Introduction to Structured Population Dynamics , Philadelphia : SIAM .
  • Diekmann , O. , Jabin , P. E. , Mischler , S. and Perthame , B. 2005 . The dynamics of adaptation: An illuminating example and a Hamilton–Jacobi approach . Theoret. Popul. Biol. , 67 : 257 – 271 .
  • Farkas , J. Z. and Hagen , T. 2009 . Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback . Commun. Pure Appl. Anal. , 8 : 1825 – 1839 .
  • Heijmans , H. 1986 . “ The dynamical behavior of the age-size distribution of a cell population ” . In The Dynamics of Physiologically Structured Populations , Edited by: Metz , J. A.J. and Diekmann , O. 185 – 202 . Berlin : Springer . Lecture Notes in Biomathematics Vol. 68
  • Henson , S. M. and Hallam , T. G. 1994 . Survival of the fittest: Asymptotic competitive exclusion in structured population and community models . Nonlinear World , 1 : 385 – 402 .
  • Hofbauer , J. and Sigmund , K. 2003 . Evolutionary game dynamics . Bull. Am. Math. Soc. , 40 : 479 – 519 .
  • Jabin , P.-E. , Lemesle , V. and Aurelle , D. 2008 . A continuous size-structured red coral growth model . Math. Models Methods Appl. Sci. , 18 : 1927 – 1944 .
  • Leenheer , P. De. and Pilyugin , S. S. 2008 . Multistrain virus dynamics with mutations: A global analysis . Math. Med. Biol. , 25 : 285 – 322 .
  • Metz , J. A.J. and Diekmann , O. 1986 . The Dynamics of Physiologically Structured Populations , Berlin : Springer . Lecture Notes in Biomathematics Vol. 68
  • Rong , L. , Feng , Z. and Perelson , A. S. 2007 . Emergence of HIV-1 drug resistance during antiretroviral treatment . Bull. Math. Biol. , 69 : 2027 – 2060 .
  • Salceanu , P. L. 2010 . “ Lyapunov exponents and persistence in dynamical systems with applications to some discrete time models ” . Proquest Dissertations and Theses 2010, 110 pages, Ph.D. diss., Arizona State University, Arizona, USA, 2009. Publication Number: AAT 3371233. Source: DAI-B 70/08, February
  • Salceanu , P. L. and Smith , H. L. 2009 . Lyapunov exponents and persistence in discrete dynamical systems . Discrete Contin. Dyn. Syst. B , 12 : 187 – 203 .
  • Salceanu , P. L. and Smith , H. L. Lyapunov exponents and uniform weak normally repelling invariant sets . Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2009) . September , Valencia, Spain. pp. 17 – 27 . Lecture Notes in Control and Informational Sciences
  • Smith , H. L. and Thieme , H. 2011 . Dynamical Systems and Population Persistence , Providence, R.I : American Mathematical Society .
  • Smith , H. L. and Waltman , P. 1999 . Perturbation of a globally stable steady state . Proc. Am. Math. Soc. , 127 : 447 – 453 .
  • Smith , H. L. and Waltman , P. 2003 . The Theory of the Chemostat , New York : Cambridge University Press .
  • Smith , H. L. and Zhao , X.-Q. 2001 . Robust persistence for semi-dynamical systems . Nonlinear Anal. , 47 : 6169 – 6179 .
  • Thieme , R. H. 2003 . Mathematics in Population Biology , NJ : Princeton University Press .
  • Verhulst , F. 1990 . Nonlinear Differential Equations and Dynamical Systems , New York : Springer .
  • Webb , G. F. 2008 . “ Population models structured by age, size and spatial position ” . In Structured Population Models in Biology and Epidemiology , Edited by: Magal , P. and Ruan , S. 1 – 49 . Berlin, Heidelberg : Springer .
  • Zhao , X.-Q. 2003 . Dynamical Systems in Population Biology , New York : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.