On the formulation and analysis of general deterministic structured population models: II. Nonlinear theory

Journal of Mathematical Biology

Volumn 43, Issue 2, 2001, Pages 157-189

  Diekmann, O ^a   Gyllenberg, M ^b   Huang, H ^c   Kirkilionis, M ^d   Metz, J A J ^e,f   Thieme, H R ^g  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITY OF TURKU   (Finland)

^c BEIJING NORMAL UNIVERSITY   (China)

^d UNIVERSITY OF HEIDELBERG   (Germany)

^e LEIDEN UNIVERSITY   (Netherlands)

^f INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS   (Austria)

^g ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Cannibalism; Deterministic at population level; Nonlinear feedback via the environment; Physiological structure; Population dynamics

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CANNIBALISM; NONLINEAR SYSTEM; POPULATION DYNAMICS;

ANIMALS; CANNIBALISM; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; POPULATION DYNAMICS;

EID: 0035433541     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850170002     Document Type: Article

References (16)

1. Calsina, À., Saldaña, J.: A model of physiologically structured population dynamics with a nonlinear individual growth rate, J. Math. Biol., 33, 335-364 (1995)
2. Calsina, À., Saldaña, J.: Asymptotic behaviour of a model of hierarchically structured population dynamics, J. Math. Biol., 35, 967-987 (1997)
3. Diekmann, O., Gyllenberg, M., Thieme, H.R.: Perturbing semigroups by solving Stieltjes renewal equations. Differential and Integral Equations, 6, 155-181 (1993a)
4. Diekmann, O., Gyllenberg, M., Metz, J.A.J., Thieme, H.R.: The "cumulative" formulation of (physiologically) structured population models, In Evolution Equations, Control Theory and Biomathematics, Ph. Clément and G. Lumer (Eds.), Marcel Dekker, New York, pp. 145-154 (1993b)
5. Diekmann, O., Gyllenberg, M., Thieme, H.R.: Perturbing evolutionary systems by step responses and cumulative outputs. Differential and Integral Equations, 8, 1205-1244 (1995)
6. Diekmann, O., Gyllenberg, M., Metz, J.A.J., Thieme, H.R.: On the formulation and analysis of general deterministic structured population models: I Linear theory. J. Math. Biol., 36, 349-388 (1998)
7. Diekmann, O., Gyllenberg, M., Thieme, H.R.: Lack of uniqueness in transport equations with a nonlocal nonlinearity, Mathematical Models and Methods in Applied Sciences, 10, 581-592 (2000)
8. Dieudonné, J.: Foundations of Modern Analysis, Enlarged and Corrected Printing, Academic Press, New York (1969)
9. Gurtin, M.E., MacCamy, R.C. Non-linear age-dependent population dynamics, Arch. Rat. Mech. Anal., 54, 281-300 (1974)
10. Gyllenberg, M., Hanski, I., Hastings, A.: Structured metapopulation models, in Metapopulation dynamics: Ecology, genetics and evolution (I. Hanski and M. Gilpin, eds.), Academic Press, London, 93-122 (1997)
11. Kirkilionis, M., Diekmann, O., Lisser, B., Nool, M., de Roos, A.M., Sommeijer, B.: (preprint). Numerical continuation of equilibria of physiologically structured population models. I. Theory.
12. Kooijman, S.A.L.M.: Dynamic Energy and Mass Budgets in Biological Systems, Cambridge University Press, Cambridge (2000)
13. Metz, J.A.J., Diekmann, O.: The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics 68. Springer, Berlin (1986)
14. Thieme, H.R.: Well-posedness of physiologically structured population models for Daphnia magna, Journal of Mathematical Biology, 26, 299-317 (1988)
15. Tucker, S.L., Zimmermann, S.O.: A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables, SIAM J. Appl. Math., 48: 549-591 (1988)
16. Webb, G.F.: (1985) Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York.