Global stability of predator-prey system with alternative prey

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Predator-prey interactions are fundamental to ecosystem stability.
• The presence of alternative prey can significantly alter these dynamics.
• Understanding stability conditions is key to predicting population fluctuations.

Purpose of the Study:

• To propose and analyze a mathematical predator-prey model incorporating alternative prey.
• To determine the conditions for the existence and stability of interior equilibrium points.
• To investigate the impact of predator foraging parameters on model stability.

Main Methods:

• Development of a mathematical model for predator-prey interactions with alternative prey.
• Derivation of analytical conditions for local and global stability of interior equilibria.
• Application of bifurcation analysis with respect to predator's searching rate and handling time.

Main Results:

• Conditions for the existence and local stability of interior equilibrium points were established.
• Global stability conditions for interior equilibrium points were successfully derived.
• Bifurcation analysis demonstrated that alternative prey presence enhances global stability.

Conclusions:

• The proposed model provides insights into the role of alternative prey in stabilizing predator-prey systems.
• Predator foraging parameters, specifically searching rate and handling time, critically influence ecosystem stability.
• The study confirms that alternative prey can lead to more robust and globally stable ecological dynamics.