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

Persistence and global stability for a class of discrete time structured population models
Pages: 4627 - 4646, Issue 10, October 2013

doi:10.3934/dcds.2013.33.4627      Abstract        References        Full text (425.0K)                  Related Articles

Hal L. Smith - School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, United States (email)
Horst R. Thieme - School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States (email)

1 H. Caswell, "Matrix Population Models, Construction, Analysis, and Interpretation," 2nd ed., Sinauer Assoc. Inc., Sunderland MA, 2001.
2 J. M. Cushing, "An Introduction to Structured Population Dynamics," CBMS-NSF Regional Conf. Series in Applied Math. 71, SIAM, Philadelphia, PA, 1998.       
3 J. M. Cushing and Y. Zhou, The net reproductive value and stability in matrix population models, Nat. Res. Mod., 8 (1994), 297-333.
4 N. Davydova, O. Diekmann and S. van Gils, On circulant populations. I. The algebra of semelparity, Lin. Alg. Appl., 398 (2005), 185-243.       
5 W. Desch and W. Schappacher, Linearized stability for nonlinear semigroups, Differential Equations in Banach Spaces (A. Favini, E. Obrecht, eds.), 61-73, Lecture Notes in Mathematics 1223, Springer, Berlin Heidelberg, (1986).       
6 O. Diekmann, N. Davydova and S. van Gils, On a boom and bust year class cycle, J. Difference Equ. Appl., 11 (2005), 327-335.       
7 O. Diekmann and Ph. Getto, Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations, J. Diff. Equations, 215 (2005), 268-319.       
8 O. Diekmann, Ph. Getto and M. Gyllenberg, Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars, SIAM J. Math. Anal., 39 (2007/08), 1023-1069.       
9 O. Diekmann, M. Gyllenberg, H. Huang, M. Kirkilionis, J. A. J. Metz and H. R. Thieme, On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory, J. Math. Biol., 43 (2001), 157-189.       
10 O. Diekmann, M. Gyllenberg and J. A. J. Metz, Steady-state analysis of structured population models, Theor. Pop. Biol., 63 (2003), 309-338.
11 O. Diekmann, M. Gyllenberg, J. A. J. Metz and H. R. Thieme, On the formulation and analysis of general deterministic structured population models. I. Linear theory, J. Math. Biol., 36 (1998), 349-388.       
12 O. Diekmann, M. Gyllenberg, J. A. J. Metz, S. Nakaoka and A. M. de Roos, Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example, J. Math. Biol., 61 (2010), 277-318.       
13 O. Diekmann, M. Gyllenberg and H. R. Thieme, Lack of uniqueness in transport equations with a nonlocal nonlinearity, Math. Models Methods Appl. Sci., 10 (2000), 581-591.       
14 O. Diekmann and S. A. van Gils, On the cyclic replicator equation and the dynamics of semelparous populations, SIAM J. Appl. Dyn. Sys., 8 (2009), 1160-1189.       
15 O. Diekmann, S. A. van Gils and S. M. Verduyn Lunel, "Delay Equations: Functional-, Complex-, and Nonlinear Analysis," Springer, New York, 1995.       
16 O. Diekmann, Y. Wang and P. Yan, Carrying simplices in discrete competitive systems and age-structured semelparous populations, Discrete Contin. Dyn. Syst., 20 (2008), 37-52.       
17 J. K. Hale, "Asymptotic Behavior of Dissipative Systems," American Mathematical Society, Providence 1988.       
18 H. J. A. M. Heijmans, Some results from spectral theory, in "One-Parameter Semigroups" (eds. Ph. Clément, et al.), North-Holland, Amsterdam, (1987), 282-291.
19 M. A. Krasnosel'skij, "Positive Solutions of Operator Equations," Noordhoff, Groningen, 1964.       
20 M. A. Krasnosel'skij, Je. A. Lifshits and A. V. Sobolev, "Positive Linear Systems: The Method of Positive Operators," Heldermann Verlag, Berlin, 1989.       
21 C.-K. Li and H. Schneider, Applications of Perron-Frobenious theory to population dynamics, J. Math. Biol., 44 (2002), 450-462.       
22 R. Rebarber, B. Tenhumberg and S. Townley, Global asymptotic stability of density dependent integral population projection models, Theoretical Population Biology, 81 (2012), 81-87.
23 H. H. Schaefer, "Topological Vector Spaces," Springer-Verlag, New York, 1971.       
24 H. L. Smith, The discrete dynamics of monotonically decomposable maps, J. Math. Biology, 53 (2006), 747-758.       
25 H. L. Smith and H. R. Thieme, "Dynamical Systems and Population Persistence," Graduate Studies in Mathematics, 118, American Mathematical Society, Providence R.I. 2011.       
26 H. R. Thieme, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol., 8 (1979), 173-187.       
27 H. R. Thieme, Well-posedness of physiologically structured population models for Daphnia magna (How biological concepts can benefit by abstract mathematical analysis), J. Math. Biology, 26 (1988), 299-317.       
28 H. R. Thieme, "Mathematics in Population Biology," Princeton University Press, Princeton 2003.       
29 H. R. Thieme, Spectral bound and reproduction number for infinite dimensional population structure and time-heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211.       
30 K. Yosida, "Functional Analysis," Springer, Heidelberg, New York, 1968.       
31 E. Zeidler. "Nonlinear Functional Analysis and Its Applications," I Springer-Verlag, New York, 1993.

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