Effects of additional food in a delayed predator-prey model

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Predator-prey systems are fundamental to ecological stability.
• Gestation delays and habitat complexity significantly influence population dynamics.
• Understanding how external factors affect these systems is crucial for conservation.

Purpose of the Study:

• To investigate the impact of supplementary predator food on a gestation delay predator-prey model.
• To analyze the role of habitat complexity in modulating these effects.
• To determine methods for controlling population fluctuations.

Main Methods:

• A mathematical model incorporating gestation delay and habitat complexity was developed.
• Time delay was used as a bifurcation parameter to analyze stability.
• Hopf bifurcation analysis and normal form theory were applied.
• Simulations were performed using experimental parameter values.

Main Results:

• Supplementary food benefits predator growth but reduces attack rates on prey.
• Both supplementary food and habitat complexity can control population fluctuations.
• Hopf bifurcation occurs at a critical delay, dependent on food supply.
• Predator population variations significantly impact system dynamics.

Conclusions:

• Supplementary feeding is a viable strategy for managing predator populations and stabilizing ecosystems.
• Habitat complexity plays a key role in mediating predator-prey interactions.
• The findings offer insights into ecological control mechanisms and conservation strategies.