Limit cycle oscillations of the human population

Area of Science:

• Mathematical Biology
• Population Dynamics
• Demography

Background:

• Traditional population models often assume constant fertility and mortality rates.
• The Easterlin hypothesis suggests that the size of one's birth cohort impacts fertility decisions.

Purpose of the Study:

• To develop and investigate a mathematical model for age-structured population growth.
• To incorporate cohort size effects on fertility into population dynamics.
• To explore the potential for population oscillations within this framework.

Main Methods:

• Development of an age-structured population model.
• Inclusion of a fertility function dependent on the size of the individual's birth cohort.
• Mathematical analysis to identify conditions for population oscillations (limit cycles).
• Validation using 20th-century United States birth data.

Main Results:

• The model demonstrates that incorporating cohort size effects on fertility can lead to self-excited, persistent oscillations in population birth rates.
• These oscillations are mathematically described as limit cycles.
• The model's predictions align with observed variations in U.S. birth numbers throughout the 20th century.

Conclusions:

• Age-structured population models that account for cohort size effects on fertility can generate realistic population fluctuations.
• The findings support the Easterlin hypothesis's relevance in understanding demographic trends.
• This model offers a more realistic approach than static models, paving the way for further refinements.