Global analysis of a predator-prey model with variable predator search rate.

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• The classical Holling-type II predator-prey model assumes constant predator search rates.
• This assumption can lead to ecological instability, such as the paradox of enrichment.

Purpose of the Study:

• To analyze a modified Holling-type II predator-prey model with prey-dependent predator search rates.
• To investigate the global behavior and stability of this modified model.
• To compare its dynamics with the classical Holling-type II model, focusing on the paradox of enrichment.

Main Methods:

• Mathematical modeling of predator-prey interactions.
• Global stability analysis of the model's equilibrium points.
• Investigation of limit cycle existence and stability.

Main Results:

• The modified model exhibits a dichotomy: either a globally stable coexistence steady state or a globally stable limit cycle.
• The paradox of enrichment, a common issue in the classical model, does not always occur in this modified version.
• Predator adaptation by lowering search rates can stabilize the system, even when the paradox of enrichment is present.

Conclusions:

• The modified Holling-type II model offers a more nuanced understanding of predator-prey dynamics.
• Prey-dependent search rates can mitigate or prevent the paradox of enrichment.
• This adaptive predator behavior is crucial for maintaining ecological stability.