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Cycles in nonlinear age-structured models. I. Renewal equations.

S Tuljapurkar1

  • 1Physics/Environmental Science, Portland University, Oregon 97207.

Theoretical Population Biology
|August 1, 1987
PubMed
Summary

This study introduces analytical tools for nonlinear renewal equations to understand population cycles. The research clarifies the dynamics, stability, and form of these cycles, with applications to human population models.

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Response.

Science (New York, N.Y.)·1995

Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Nonlinear Dynamics

Background:

  • Density-dependent population models are often nonlinear.
  • Bifurcation can lead to sustained population cycles.
  • Understanding these cycles is crucial for ecological and demographic studies.

Purpose of the Study:

  • To develop analytical tools for nonlinear renewal equations.
  • To study sustained population cycles arising from bifurcation.
  • To explicitly describe cycle properties and stability.

Main Methods:

  • Development of analytical techniques for nonlinear renewal equations.
  • Analysis of bifurcation phenomena in population models.
  • Application to a cohort-controlled human population model.

Main Results:

  • Explicit description of bifurcation direction.
  • Characterization of the period, form, and dynamic stability of sustained cycles.
  • Illustration of results using a human population model formalizing the Easterlin effect.

Conclusions:

  • The developed analytical tools provide a comprehensive understanding of population cycle dynamics.
  • The findings offer insights into the behavior of cohort-controlled human populations.
  • This work contributes to the theoretical framework for analyzing complex population dynamics.

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