Population models with delays

  • Mimmo Iannelli
  • Andrea Pugliese
Part of the UNITEXT book series (UNITEXT, volume 79)


The possibility that events, lost in the past, still influence our lives, is an evocative notion, strongly inspiring literature, at least. The character of the tale by Italo Calvino, quoted in the foreword, is in fact obsessed by some event happened millions of years before, within an hallucinatory mixture of space and time. However, the need of including the influence of past effects in the description of natural phenomena was explicitly recognized by Vito Volterra in a lecture in 1912 ([8]), where we read 2:


Periodic Solution Hopf Bifurcation Scramble Competition Renewal Equation Fading Memory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bellman, R., Cooke, K.L.: Differential-Difference Equations. Academic Press, New York (1963)zbMATHGoogle Scholar
  2. 2.
    Brauer, F., Castillo-Chávez, C.: Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics 40, Springer-Verlag Berlin Heidelberg (2000)Google Scholar
  3. 3.
    Cushing, J.M.: Integrodifferential Equations and Delay Models in Population Dynamics. Lectures Notes in Biomathematics 20, Springer-Verlag Berlin Heidelberg (1977)Google Scholar
  4. 4.
    Hutchinson, G.E.: Circular causal systems in ecology. Ann. N.Y. Acad. Sci. 50, 221–246 (1948)CrossRefGoogle Scholar
  5. 5.
    Nicholson, A.J.: An outline of the dynamics of animal populations. Aust. J. Zoo. 2 9–65 (1954)CrossRefGoogle Scholar
  6. 6.
    Nicholson, A.J.: The self-adjustment of populations to change. Cold Spring Harb. Symp. Quant. Biol. 22, 153–173 (1957)CrossRefGoogle Scholar
  7. 7.
    de Roos, A.M., Persson, L.: Population and Community Ecology of Ontogenetic Development. Princeton University Press, New Jersey (2013)CrossRefGoogle Scholar
  8. 8.
    Volterra, V.: L'applicazione del calcolo ai fenomeni di ereditá. in Saggi Scientifici, Zanichelli, Bologna (1920)Google Scholar
  9. 9.
    Volterra, V.: Sulle fluttuazioni biologiche. Rendiconti della R. Accademia Nazionale dei Lincei, ser. VI, vol V, 3–10 (1927)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mimmo Iannelli
    • 1
  • Andrea Pugliese
    • 1
  1. 1.Department of MathematicsUniversity of TrentoItaly

Personalised recommendations