Physiologically Structured Population Models: Towards a General Mathematical Theory

作者: Odo Diekmann , Mats Gyllenberg , Johan Metz

DOI: 10.1007/978-3-540-34428-5_2

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摘要: We review the state-of-the-art concerning a mathematical framework for general physiologically structured population models. When individual development is affected by density, such models lead to quasilinear equations. show how associate dynamical system (defined on an infinite dimensional state space) model and determine steady states. Concerning principle of linearized stability, we offer conjecture as well some preliminary steps towards proof.

参考文章(21)
W. Desch, W. Schappacher, Linearized stability for nonlinear semigroups Springer Berlin Heidelberg. pp. 61- 73 ,(1986) , 10.1007/BFB0099183
Susan L. Tucker, Stuart O. Zimmerman, A Nonlinear Model of Population Dynamics Containing an Arbitrary Number of Continuous Structure Variables Siam Journal on Applied Mathematics. ,vol. 48, pp. 549- 591 ,(1988) , 10.1137/0148032
Àngel Calsina, Joan Saldaña, ASYMPTOTIC BEHAVIOUR OF A MODEL OF HIERARCHICALLY STRUCTURED POPULATION DYNAMICS Journal of Mathematical Biology. ,vol. 35, pp. 967- 987 ,(1997) , 10.1007/S002850050085
Marten Scheffer, Steve Carpenter, Jonathan A. Foley, Carl Folke, Brian Walker, Catastrophic shifts in ecosystems Nature. ,vol. 413, pp. 591- 596 ,(2001) , 10.1038/35098000
Jan Prüβ, Stability analysis for equilibria in age-specific population dynamics Nonlinear Analysis-theory Methods & Applications. ,vol. 7, pp. 1291- 1313 ,(1983) , 10.1016/0362-546X(83)90002-0
AndréM. de Roos, Lennart Persson, Horst R. Thieme, Emergent Allee effects in top predators feeding on structured prey populations. Proceedings of The Royal Society B: Biological Sciences. ,vol. 270, pp. 611- 618 ,(2003) , 10.1098/RSPB.2002.2286