[Logistic effects in the two-sex model with "harmonic mean" fertility function]

Area of Science:

• Population dynamics
• Mathematical biology
• Population genetics

Context:

• Investigating population stability requires understanding sex-ratio dynamics.
• Fertility functions significantly influence population equilibrium.
• Logistic terms introduce density-dependent effects crucial for realism.

Purpose:

• To analyze the impact of logistic terms on a two-sex random mating model.
• To determine the stability of equilibrium points in population models.
• To explore the role of harmonic mean fertility in population dynamics.

Summary:

• The study examines a two-sex random mating model incorporating logistic terms and harmonic mean fertility.
• Phase plane analysis reveals a unique, globally stable equilibrium point.
• This stable point represents the final population adjustment, following an initial sex composition balancing period.

Impact:

• Provides insights into the long-term stability of populations with balanced sex ratios.
• Highlights the importance of density-dependent factors in population modeling.
• Offers a theoretical framework for understanding population adjustment processes.