A nonautonomous juvenile-adult model: Well-posedness and long-time behavior via a comparison principle

SIAM Journal on Applied Mathematics

Volumn 69, Issue 6, 2009, Pages 1644-1661

  Ackleh, Azmy S ^a   Deng, Keng ^a  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

Comparison principle; Continuous juvenile adult model; Existence uniqueness; Extinction; Uniform persistence

Indexed keywords

COMPARISON PRINCIPLE; CONTINUOUS JUVENILE-ADULT MODEL; EXISTENCE-UNIQUENESS; EXTINCTION; UNIFORM PERSISTENCE;

EID: 67349138475     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/080723673     Document Type: Article

References (33)

1. A. S. ACKLEH, H. T. BANKS, AND K. DENG, A difference approximation for a coupled system of nonlinear size-structured populations, Nonlinear AnaI., 50 (2002), pp. 727-748.
2. A. S. ACKLEH AND P. DELEENHEER, Discrete three-stage population model: Persistence and global stability results, J. Biol. Dynamics, 2 (2008), pp. 415-427.
3. A. S. ACKLEH AND K. DENG, A monotone approximation for the nonautonomous sizestructured population model, Quart. AppI. Math., 57 (1999), pp. 261-267.
4. A. S. AKLEH 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), pp. 1-15.
5. A. S. ACKLEH AND K. DENG, Survival of the fittest in a quasilinear size-structured population model, Natural Resource Modelling, 17 (2004), pp. 213-228.
6. A. S. ACKLEH, K. DENG, AND X. WANG, Competitive exclusion and coexistence in a quasilinear size-structured population model, Math. Biosci., 192 (2004), pp. 177-192.
7. A. S. ACKLEH, Y. DIB, AND S. JANG, A three-stage discrete-time population model: Seasonal versus continuous reproduction, J. Biol. Dynamics, 1 (2007), pp. 305-319.
8. A. S. ACKLEH AND K. ITO, An implicit finite difference scheme for the nonlinear size-structured population model, Numer. Funct. Anal. Optim., 18 (1997), pp. 865-884.
9. A. S. ACKLEH AND S. JANG, A discrete two-stage population model: Continuous versus seasonal reproduction, J. Differ. Equations Appl., 13 (2007), pp. 261-274.
10. R. BELLMAN, Methods of Nonlinear Analysis, Vol. II, Academic Press, New York, 1973.
11. A. CALSINA AND J. SALDANA, A model of physiologically structured population dynamics with a nonlinear individual growth rate, J. Math. Biol., 33 (1995), pp. 335-364.
12. A. CALSINA AND J. SALDAÑA, Global dynamics and optimal life history of a structured population model, SIAM J. Appl. Math., 59 (1999), pp. 1667-1685.
13. J. M. CUSHING, The dynamics of hierarchical age-structured populations, J. Math. Biol., 32 (1994), pp. 705-729.
14. J. M. CUSHING, A juvenile-adult model with periodic vital rates, J. Math. Biol., 53 (2006), pp. 520-539.
15. J. M. CUSHING AND J. LI, Juvenile versus adult competition, J. Math. Biol., 29 (1991), pp. 457-473.
16. J. P. COLLINS AND A. STORFER, Amphibian decline: Sorting the hypothesis, Diversity Distributions, 9 (2003), pp. 89-98.
17. O. DIEKMANN, P. 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), pp. 1023-1069.
18. 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), pp. 157-189.
19. 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), pp. 349-388.
20. J. FARKAS AND T. HAGEN, Asymptotic behavior of size-structured population via juvenile-adult interaction, Discrete Contin. Dynam. Systems Ser. B, 9 (2008), pp. 249-266.
21. J. S. GARTON AND R. A. BRANDON, Reproductive ecology of the H. cinerea, Hyla cinerea, in southern Illinois (anura: hylidae), Herpetologica, 31 (1975), pp. 150-161.
22. M. S. GUNZBURGER, Reproductive ecology of the H. cinerea (Hyla cinerea) in northwestern Florida, Amer. Midland Naturalist, 155 (2006), pp. 321-328.
23. M. IANNELLI, Mathematical Theory of Age-Structured Population Dynamics, Giardini Editori, Pisa, Italy, 1994.
24. G. S. LADDE, V. LAKSHMIKANTHAM, AND A. S. VATSALA, Monotone Rerative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985.
25. C. V. PAO, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
26. L. PHAM, S. BOUDREAUX, S. KARHBET, B. PRICE, A. S. ACKLEH, J. CARTER, AND N. PAL, Population estimates of Hyla cinerea (Schneider) (green tree frog) in an urban environment, Southeastern Naturalist, 6 (2007), pp. 203-216.
27. E. SHIM, Z. FENG, C. CASTILLO-CHAVEZ, and M. MARTCHEVA, An age-structured epidemic model of rotavirus with vaccination, J. Math. Biol., 53 (2006), pp. 719-746.
28. K. T. SMITH, Effects of nonindigenous tadpoles on native tadpoles in Florida: Evidence of competition, Biol. Conservation, 123 (2005), pp. 433-441.
29. A. STORFER, Amphibian decline: Future directions, Diversity Distributions, 9 (2003), pp. 151-163.
30. H. THIEME, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), pp. 755-763.
31. J. R. VONESH AND O. D. L. CRUZ, Complex life cycles and density dependence: Assessing the contribution of egg mortality to amphibian declines, Oecologia, 133 (2002), pp. 325-333.
32. G. F. WEBB, Theory of Nonlinear Age-Dependent Population Dynamics, Monogr. Textbooks Pure AppI. Math. 89, Marcel Dekker, New York, 1985.
33. A. H. WRIGHT AND A. A. WRIGHT, Handbook of Frogs and Toads of the United States and Canada, Comstock Publishing Company, Ithaca, NY, 1949.