Hunting cooperation in a prey-predator model with maturation delay

Area of Science:

• Ecological dynamics
• Mathematical biology
• Population ecology

Background:

• Prey-predator models are crucial for understanding ecological stability.
• Cooperative hunting and maturation delays are key factors influencing population dynamics.
• Investigating these factors can reveal complex ecological interactions and stability boundaries.

Purpose of the Study:

• To analyze a prey-predator model incorporating cooperative hunting and predator maturation delay.
• To determine the influence of hunting time and cooperation rates on species coexistence.
• To examine the impact of maturation delay on predator population stability and system bifurcations.

Main Methods:

• Mathematical modeling of prey-predator interactions.
• Analysis of ecological system dynamics with and without maturation delay.
• Numerical simulations to explore bifurcations and stability thresholds.
• Investigating the effects of cooperation rate and hunting time parameters.

Main Results:

• Sufficient hunting time and weak predator cooperation facilitate prey-predator coexistence.
• Increasing predator maturation delay elevates the probability of predator extinction.
• Maturation delay shifts bifurcation curves and thresholds compared to the non-delayed system.
• Cooperation rate and hunting time influence the occurrence of bifurcations.

Conclusions:

• Cooperative hunting strategies and predator maturation periods significantly impact ecological stability.
• Maturation delays can destabilize predator populations, leading to potential extinction.
• The interplay between cooperative behaviors and time delays creates complex population dynamics.
• Findings provide insights into managing and conserving predator-prey systems.