Publication Cover
Mathematical Population Studies
An International Journal of Mathematical Demography
Volume 5, 1994 - Issue 1: Nonlinear Models in Demography
18
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

The cohort feedback model with symmetric net maternity

Pages 25-44 | Received 20 Jan 1994, Published online: 21 Sep 2009

References

  • Bergh , M and Getz , W. 1988 . Stability of discrete age‐structured and aggregated delay‐difference matrix population models . Journal of Mathematical Biology , 26 : 551 – 581 .
  • Bonneuil , N. 1990 . Turbulent dynamics in a VIIth century population . Mathematical Population Studies , 2 : 289 – 312 .
  • Caswell , H. 1989 . Matrix Population Models , Sunderland, MA : Sinauer Associates .
  • Caswell , H. and Weeks , D. E. 1986 . Two‐sex models: Chaos, extinction, and other dynamic consequences of sex . The American Naturalist , 128 : 707 – 735 .
  • Chow , S‐N. and Hale , J. 1982 . Methods of Bifurcation Theory , Berlin : Springer‐Verlag .
  • Chung , R. 1990 . Cycles in the Two‐Sex Problem , Berkeley : Department of Demography, University of California . Ph.D. dissertation
  • Coale , A. 1972 . The Growth and Structure of Human Populations , Princeton University Press .
  • Cushing , J. M. 1978 . Nontrivial periodic solutions of some Volterra integral equations . Springer Lecture Notes in Mathematics , 737 : 50 – 66 .
  • Dunford , N and Schwartz , J. T. 1958 . Linear Operators , Vol. 1 , New York : Interscience Publishers .
  • Feichtinger , G. and Sorger , G. 1990 . Capital accumulation, aspiration adjustment, and population growth: Limit cycles in an Easterlin‐type model . Mathematical Population Studies , 2 : 93 – 104 .
  • Frauenthal , J. and Swick , K. 1983 . Limit cycle oscillations of the human population . Demography , 20 : 285 – 298 .
  • Folland , G. B. 1984 . Real Analysis , New York : John Wiley and Sons .
  • Guckenheimer , J. , Oster , G. and Ipaktchi , A. 1977 . The dynamics of density‐dependent population models . Journal of Mathematical Biology , 4 : 101 – 147 .
  • Gurtin , M. E. and MacCamy , R. C. 1974 . Non‐linear age‐dependent population dynamics . Archive for Rational Mechanics and Analysis , 54 : 281 – 300 .
  • Hale , J. de Oliviera . 1980 . Hopf bifurcation for functional equations . Journal of Mathematical Analysis and Applications , 74 : 41 – 59 .
  • Iooss , G. 1979 . Bifurcation of Maps and Applications , Amsterdam : North Holland Publishing Company .
  • Lee , R. D. 1974 . The formal dynamics of controlled populations and the echo, the boom, and the bust . Demography , 11 : 563 – 585 .
  • Levin , S. and Goodyear , C. 1980 . Analysis of an age‐structured fishery model . Journal of Mathematical Biology , 9 : 245 – 274 .
  • Mazja , V. 1985 . Sobolev Spaces , Edited by: Saposnikova , T. Berlin : Springer Verlag .
  • May , R. 1974 . Biological populations with nonoverlapping generations: Stable points, stable cycles, and chaos . Science , 186 : 645 – 647 .
  • Prshawetz , A. and Feichtinger , G. 1992 . Endogenous population growth may imply chaos , Forschungs‐bericht 149 Vienna : Institut fuer Oekonometrie, Operations Research, und Systemtheorie, Technische Univer‐sitaet .
  • Samuelson , P. 1976 . An economist's non‐linear model of self‐generated fertility waves . Population Studies , 30 : 243 – 247 .
  • Sobolev , S. 1991 . Some Applications of Functional Analysis in Mathematical Physics, , Third Edition , AMS Translations of Mathematical Monographs 90 Edited by: McFadden , H. Providence, RI : American Mathematical Society .
  • Stein , E. 1970 . Singular Integrals and Differentiability Properties of Functions , Princeton, NJ : Princeton University Press .
  • Swick , K. 1981 . Stability and bifurcation in age‐dependent population dynamics . Theoretical Population Biology , 20 : 80 – 100 .
  • Staffans , O. J. 1987 . Hopf bifurcation for functional and functional differential equations with infinite delay . Journal of Differential Equations , 70 : 114 – 151 .
  • Tuljapurkar , S. 1987 . Cycles in nonlinear age‐structured models I. Renewal equations . Theoretical Population Biology , 32 : 26 – 40 .
  • Wachter , K. W. 1991 . Elusive cycles: Are there dynamically possible Lee‐Easterlin models for U.S. births? . Population Studies , 45 : 109 – 135 .
  • Wachter , K. W. 1991 . Pre‐procreative ages in population stability and cyclicity . Mathematical Population Studies , 3 : 79 – 104 .
  • Wachter , K. W. and Lee , R. D. 1989 . U.S. births and limit cycle models . Demography , 26 : 99 – 115 .
  • Wachter , K. W. and Lee , R. D. 1987 . American limit cycle oscillations? , Sloan Working Paper in Population Studies #10 Berkeley : Institute of International Studies, University of California .
  • Webb , G. E. 1985 . Theory of Nonlinear Age‐Dependent Population Dynamics , Basel : Marcel Dekker .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.