Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Extinction and uniform strong persistence of a size-structured population model
Pages: 831 - 840, Issue 3, May 2017

doi:10.3934/dcdsb.2017041      Abstract        References        Full text (364.5K)           Related Articles

Keng Deng - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, United States (email)
Yixiang Wu - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States (email)

1 A. S. Ackleh and K. Deng, Existence-uniqueness of solutions for a nonlinear nonautonomous size-structured population model: an upper-lower solution approach, Canadian Appl. Math. Quart., 8 (2000), 1-15.       
2 H. T. Banks, S. L. Ernstberger and S. Hu, Sensitivity equations for a size-structured population model, Quart. Appl. Math., 67 (2009), 627-660.       
3 H. T. Banks and F. Kappel, Transformation semigroups and $L^1$-approximation for size structure population models, Semigroup Forum, 38 (1989), 141-155.       
4 H. T. Banks, F. Kappel and C. Wang, A semigroup formulation of a nonlinear size-structured distributed rate population model, Internat. Ser. Numer. Math., 118 (1994), 1-19.       
5 A. Calsina and J. Saldana, A model of physiologically structured population dynamics with a nonlinear individual growth rate, J. Math. Biol., 33 (1995), 335-364.       
6 A. Calsina and M. Sanchon, Stability and instability of equilibria of an equation of size structured population dynamics, J. Math. Anal. Appl., 286 (2003), 435-452.       
7 K. Deng and Y. Wang, Sensitivity analysis for a nonlinear size-structured population model, Quart. Appl. Math., 73 (2015), 401-417.       
8 J. Z. Farkas, Stability conditions for a non-linear size-structured model, Nonlinear Anal. Real World Appl., 6 (2005), 962-969.       
9 J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. Appl., 328 (2007), 119-136.       
10 Z. Feng and H. R. Thieme, Endemic models with arbitrarily distributed periods of infection I: Fundamental properties of the model, SIAM J. Appl. Math., 61 (2000), 803-833.       
11 Z. Feng, L. Rong and R. K. Swihart, Dynamics of an age-structured metapopulation model, Natural Resource Modeling, 18 (2005), 415-440.       
12 M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Giardini Editori e Stampatori, Pisa, 1995.
13 J. A. J. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, Lecture Notes in Biomath., 68, Springer-Verlag, Berlin, 1986.       
14 H. Thieme, Uniform weak implies uniform strong persistence for non-autonomous semiflows, Proc. Amer. Math. Soc., 127 (1999), 2395-2403.       

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