Optimal harvesting policy for single population with periodic coefficients

Area of Science:

• Population Dynamics
• Mathematical Ecology
• Resource Management

Background:

• The logistic equation is a fundamental model in population dynamics.
• Periodic coefficients in population models reflect environmental fluctuations.
• Sustainable yield optimization is crucial for renewable resource management.

Purpose of the Study:

• To analyze a time-dependent logistic equation with periodic coefficients.
• To determine optimal harvesting policies for maximizing annual-sustainable yield.
• To generalize existing models for population management.

Main Methods:

• Analysis of a unique positive periodic solution for the logistic equation.
• Investigation of optimal harvesting policies (constant and periodic).
• Derivation of explicit expressions for optimal population levels and yields.

Main Results:

• A unique, globally stable positive periodic solution was identified.
• Optimal constant and periodic harvest efforts were determined.
• Explicit formulas for maximum annual-sustainable yield were derived.

Conclusions:

• The study provides a generalized framework for managing populations with time-varying dynamics.
• Optimal harvesting strategies can be explicitly determined for periodic logistic models.
• Results extend classical population management theories to more complex scenarios.