On discrete time Beverton-Holt population model with fuzzy environment

Area of Science:

• Ecology
• Mathematical Biology
• Dynamical Systems

Background:

• Population dynamics are often modeled using deterministic equations.
• Real-world population data can exhibit inherent uncertainty.
• The Beverton-Holt model is a standard tool for fisheries and population management.

Purpose of the Study:

• To investigate the dynamical behaviors of the discrete time Beverton-Holt population model incorporating fuzzy parameters.
• To explore how fuzzy initial conditions influence population model outcomes.
• To establish conditions for boundedness, stability, and persistence in fuzzy population models.

Main Methods:

• Utilized a discrete time Beverton-Holt population model.
• Incorporated fuzzy parameters and fuzzy initial conditions.
• Applied a generalization of division (g-division) for fuzzy number arithmetic.
• Analyzed model behavior including boundedness, global asymptotic stability, and persistence.

Main Results:

• Demonstrated the model's flexibility in fitting population data with uncertainty.
• Showcased how fuzzy parameters and initial conditions affect model dynamics.
• Confirmed conditions for boundedness, global asymptotic stability, and persistence of positive solutions under fuzzy conditions.
• Validated findings through two illustrative examples.

Conclusions:

• The fuzzy parameter Beverton-Holt model offers a robust framework for analyzing population dynamics with uncertainty.
• The g-division method effectively handles fuzzy arithmetic in population modeling.
• The study provides a foundation for more realistic population modeling in ecological and management contexts.