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Modeling and analysing physiologically structured populations

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Mathematics Inspired by Biology

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References

  1. Calsina, À & J. Saldaña. 1995. A model of physiologically structured population dynamics with a nonlinear individual growth rate. J. Math. Biol.33: 335–364.

    Article  MathSciNet  MATH  Google Scholar 

  2. Calsina, À & J. Saldaña. 1997. Asymptotic behaviour of a model of hierarchically structured population dynamics. J. Math. Biol.35: 967–987.

    Article  MathSciNet  MATH  Google Scholar 

  3. Clément, Ph., O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans & H. R. Thieme. 1989. Perturbation theory for dual semigroups. III Nonlinear Lipschitz continuous perturbations in the sun-reflexive case. Volterra Integro-Differ ential Equations in Banach Spaces and Applications, G. Da Prato & M. Ianelli, Pitman Research Notes in Maths 190: 67–89.

    Google Scholar 

  4. Diekmann, O., M. Gyllenberg, J.A.J. Metz & H.R. Thieme. 1998. On the formulation and analysis of general deterministic structured population models. I. Linear Theory J. Math. Biol.36: 349–388.

    Article  MathSciNet  MATH  Google Scholar 

  5. Diekmann, O., M. Gyllenberg, H. Huang, M. Kirkilionis, J.A.J. Metz & H.R. Thieme. II. Nonlinear Theory. In preparation.

    Google Scholar 

  6. Diekmann, O. & J.A.J. Metz. 1994. On the reciprocal relationship between life histories and population dynamics. Frontiers in Mathematical Biology, S.A. Levin, Springer LNiB 100: 263–279.

    Google Scholar 

  7. Diekmann, O., M. Gyllenberg, H. R. Thieme & S.M. Verduyn Lunel. (preprint). A cell-cycle model revisited.

    Google Scholar 

  8. Diekmann, O., H.J.A.M. Heijmans & H.R. Thieme. 1984. On the stability of the cell size distribution. J. Math. Biol.19: 227–248.

    Article  MathSciNet  MATH  Google Scholar 

  9. Diekmann, O., S.A. van Gils, S.M. Verduyn Lunel & H.-O. Walther. 1995. Delay Equations: Functional-Complex and Nonlinear Analysis. Springer Verlag.

    Google Scholar 

  10. Feller, W. 1966. An Introduction to Probability Theory and Its Applications. Vol. II. Wiley.

    Google Scholar 

  11. Fisher, R.A. 1958. The Genetical Theory of Natural Selection, 2nd rev. ed., Dover.

    Google Scholar 

  12. Gripenberg, G., S-O. Londen & O. Staffans. 1990. Volterra Integral and Functional Equations. Cambridge Univ. Press.

    Google Scholar 

  13. Gyllenberg, M. 1986. The size and scar distribution of the yeast Saccharonymes cerevisiae. J. Math. Biol.24: 81–101.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Huang (personal communication)

    Google Scholar 

  15. Huyer, B. 1997. On periodic cohort solutions of a size-structured population model. J. Math. Biol.35: 908–934.

    Article  MathSciNet  MATH  Google Scholar 

  16. Jagers, P. 1991. The growth and stabilization of populations. Statistical Science6: 269–283.

    Article  MathSciNet  MATH  Google Scholar 

  17. Jagers, P. preprint. The deterministic evolution of general branching populations.

    Google Scholar 

  18. Jagers, P. 1983. On the Malthusianness of general branching processes in abstract type spaces. In: Probability and Mathematical Statistics. Essays in Honour of Carl-Gustav Esseen. Dep. Mathematics, Uppsala University.

    Google Scholar 

  19. Kirkilionis, M.A., O. Diekmann, B. Lisser, M. Nool, A.M. de Roos & B.P. Sommeijer (preprint) Numerical continuation of equilibria of physiologically structured population models. I. Theory CWI-Report MAS 9714. 1997.

    Google Scholar 

  20. Metz, J.A.J. & O. Diekmann (eds.) 1986. Dynamics of Physiologically Structured Populations. Lecture Notes in Biomath. 68. Springer Verlag.

    Google Scholar 

  21. Metz, J.A.J. & F. van den Bosch. 1995. Velocities of epidemic spread. Epidemic Models: Their Structure and Relation to Data. D. Mollison. Cambridge University Press.

    Google Scholar 

  22. Mollison, D. 1991. Dependence of epidemic and population velocities on basic parameters. Math. Biosc.107: 255–287.

    Article  MATH  Google Scholar 

  23. Nagel, R. 1986. One Parameter Semigroups of Positive Operators. Springer LNiM 1184.

    Google Scholar 

  24. de Roos, A.M., O. Diekmann & J.A.J. Metz. 1992. Studying the dynamics of structured population models: a versatile technique and its application to Daphnia. Am. Nat.139: 123–147.

    Article  Google Scholar 

  25. de Roos, A.M., 1997. A gentle introduction to physiologically structured population models. In: Tuljapurkar, S. & H. Caswell 1997. Structured-population models in marine, terrestrial, and freshwater systems. Chapman & Hall: 119–204.

    Google Scholar 

  26. Shurenkov, V.M. (preprint 1). On the existence of a Malthusian parameter.

    Google Scholar 

  27. Shurenkov, V.M. (preprint 2) On the relationship between spectral radii and Perron roots.

    Google Scholar 

  28. Shurenkov, V.M. 1984. On the theory of Markov renewal. Theory Prob. Appl.29: 247–265.

    Article  MathSciNet  MATH  Google Scholar 

  29. Shurenkov, V.M. 1992. Markov renewal theory and its applications to Markov ergodic processes. Lect. Notes Dept. of Math., Chalmers Univ. of Technology.

    Google Scholar 

  30. Thieme, H.R. 1988. Well-posedness of physiologically structured population models for Daphnia magna. J. Math. Biol.26: 299–317.

    Article  MathSciNet  MATH  Google Scholar 

  31. Tucker, S.L. & S.O. Zimmermann. 1988. A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables. SIAM. J. Appl. Math.48: 549–591.

    Article  MathSciNet  MATH  Google Scholar 

  32. Van den Bosch, F., A.M. de Roos & W. Gabriel. 1988. Cannibalism as a life boat meachanism. J. Math. Biol.26: 619–633.

    Article  MathSciNet  MATH  Google Scholar 

  33. Van den Bosch, F., J.A.J. Metz & O. Diekmann. 1990. The velocity of spatial population expansion. J. Math. Biol.28: 529–565.

    Article  MathSciNet  MATH  Google Scholar 

  34. Webb, G.F. 1985. Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, New York.

    MATH  Google Scholar 

  35. Widder, D.V. 1946. The Laplace Transform. Princeton Univ. Press.

    Google Scholar 

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Diekmann, O. (1999). Modeling and analysing physiologically structured populations. In: Capasso, V. (eds) Mathematics Inspired by Biology. Lecture Notes in Mathematics, vol 1714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092374

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  • DOI: https://doi.org/10.1007/BFb0092374

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