Pre‐procreative ages in population stability and cyclicity

References

• Ahlfors , L. 1966 . Complex Analysis, , Second Edition , New York : McGraw Hill .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Coale , A. 1972 . The Growth and Structure of Human Populations , Princeton, New Jersey : Princeton University Press .
   Google Scholar
• Coale , A. and McNeil , D. 1976 . On the asymptotic trajectory of the roots of Lotka's equation . Theoretical Population Biology , 9 : 123 – 127 .
   PubMedGoogle Scholar
• Coale , A. and Trussell , J. 1981/84 . ‘Roots’, or how a population forgets its past . Canadian Studies in Population , 8 : 1 – 25 .
   Google Scholar
• Deriso , R. B. 1980 . Harvesting strategies and parameter estimation for an age‐structured model . Canadian Journal of Fisheries and Aquatic Sciences , 37 : 268 – 282 .
   Web of Science ®Google Scholar
• Doetsch , G. 1950 . Handbuch der Laplace‐Transformation , Volume 1 , Basel : Verlag Birkhaueser .
   Google Scholar
• Frauenthal , J. and Swick , K. 1983 . Limit cycle oscillations of the human population . Demography , 20 : 285 – 298 .
   PubMed Web of Science ®Google Scholar
• Guckenheimer , J. , Oster , G. and Ipaktchi , A. 1977 . The dynamics of density dependent population models . Journal of Mathematical Biology , 4 : 101 – 147 .
   Web of Science ®Google Scholar
• Hale , J. and Oliviera , d. 1980 . Hopf bifurcation for functional equations . Journal of Mathematical Analysis and Applications , 74 : 41 – 59 .
   Web of Science ®Google Scholar
• Hille , E. 1962 . Analytic Function Theory , Volume II , Boston : Ginn and Company .
   Google Scholar
• Hoffman , K. 1962 . Banach Spaces of Analytic Functions , Englewood Cliffs, New Jersey : Prentice Hall .
   Google Scholar
• Iooss , G. 1979 . Bifurcation of Maps and Applications , Amsterdam : North Holland Publishing Company .
   Google Scholar
• Keyfitz , N. 1968 . Introduction to the Mathematics of Population , Reading, Massachusetts : Addison‐Wesley .
   Google Scholar
• Keyfitz , N. 1977 . Applied Mathematical Demography , New York : John Wiley and Sons .
   Google Scholar
• LeBras , H. 1969 . Retour d'une population a l'état stable après une ‘catastrophe’ . Population , 24 : 861 – 896 .
   Google Scholar
• Lee , R. D. 1971 . “ Econometric Studies of Topics in Demographic History ” . Harvard University, published by Arno Press . Ph.D. dissertation 1978
   Google Scholar
• Lee , R. D. 1974 . The formal dynamics of controlled populations and the echo, the boom, and the bust . Demography , 11 : 563 – 585 .
   PubMed Web of Science ®Google Scholar
• Levin , S. and Goodyear , C. 1980 . Analysis of an age‐structured fishery model . Journal of Mathematical Biology , 9 : 245 – 274 .
   Web of Science ®Google Scholar
• Rudin , W. 1970 . Real and Complex Analysis , London : McGraw Hill .
   Google Scholar
• Schnute , J. 1985 . A general theory for analysis of catch and effort data . Canadian Journal of Fisheries and Aquatic Sciences , 42 : 414 – 429 .
   Web of Science ®Google Scholar
• Staffans , O. J. 1987 . Hopf bifurcation for functional and functional differential equations with infinite delay . Journal of Differential Equations , 70 : 114 – 151 .
   Web of Science ®Google Scholar
• Swick , K. 1981 . Stability and bifurcation in age‐dependent population dynamics . Theoretical Population Biology , 20 : 80 – 100 .
   PubMed Web of Science ®Google Scholar
• Swick , K. 1985 . Some reducible models of age dependent dynamics . SIAM Journal of Applied Mathematics , 45 : 256 – 267 .
   Google Scholar
• Turner , J. C. 1976 . Calculation of roots of Lotka's equation . Theoretical Population Biology , 9 : 222 – 237 .
   PubMedGoogle Scholar
• Trussell , J. 1977 . Determinants of roots of Lotka's equation . Mathematical Biosciences , 36 : 213 – 227 .
   Google Scholar
• Wachter , K. W. 1984 . Lotka's roots under rescalings . Proceedings of the National Academy of Sciences, USA , 81 : 3600 – 3604 .
   PubMedGoogle Scholar
• Wachter , K. W. 1986 . Ergodicity and inverse projection . Population Studies , 40 : 275 – 287 .
   Web of Science ®Google Scholar
• Wachter , K. W. 1991 . Elusive Cycles: Are there dynamically possible Lee‐Easterlin models for U.S. births? . Population Studies , 45 : 109 – 135 .
   Web of Science ®Google Scholar
• Wachter , K. W. and Lee , R. D. 1987 . American Limit Cycle Oscillations? , Sloan‐Berkeley Working Paper in Population Studies #10
   Google Scholar
• Wicksell , S. D. 1931 . Nuptiality, fertility, and reproductivity . Skandinavisk Aktuarietidshift , : 125 – 157 .
   Google Scholar