A two-sex demographic model with single-dependent divorce rate

Area of Science:

• Demography
• Mathematical Biology
• Population Dynamics

Background:

• Divorce is an understudied demographic process.
• Classical two-sex models often assume a constant divorce rate.
• The influence of single population size on divorce is not well understood.

Purpose of the Study:

• To investigate the mathematical and biological implications of a divorce rate dependent on the single population.
• To modify the classical exponential two-sex model to incorporate this dependency.
• To analyze the effects on population dynamics.

Main Methods:

• Modification of the classical exponential two-sex model.
• Modeling divorce rate as an increasing function of the single population.
• Hopf bifurcation analysis to study model stability and oscillations.

Main Results:

• The modified model shows that single population pressure alters the exponential growth of the classical model.
• The total population size becomes bounded.
• A unique positive equilibrium exists, and sustained oscillations are possible.

Conclusions:

• The size of the single population significantly impacts divorce rates and population dynamics.
• The assumption of a constant divorce rate in classical models may oversimplify real-world demographic processes.
• The modified model provides a more nuanced understanding of population dynamics influenced by marital dissolution.