Dynamical behavior of two predators competing over a single prey.

Area of Science:

• Ecology
• Mathematical Biology
• Theoretical Ecology

Background:

• Food webs are critical for understanding ecosystem stability and species interactions.
• Predator-prey dynamics are fundamental to ecological theory, influencing population persistence.
• Competitive exclusion principle suggests that competing species cannot coexist indefinitely.

Purpose of the Study:

• To investigate the dynamical behavior of a food web with two predators and one prey.
• To determine conditions for the persistence and coexistence of competing predators.
• To explore the role of boundary equilibria and periodic solutions in food web stability.

Main Methods:

• Analysis of a mathematical food web model.
• Investigation of equilibrium points and stability on boundary prey-predator planes.
• Numerical simulations to explore system behavior, including periodic and quasi-periodic solutions.

Main Results:

• Competitive exclusion prevents predator persistence when boundary planes have stable equilibria.
• Numerical simulations demonstrate predator persistence is possible with periodic solutions.
• The system exhibits quasi-periodic behavior and limit cycle coexistence in the positive octant.

Conclusions:

• The principle of competitive exclusion is not universally applicable in complex food webs.
• Periodic solutions and limit cycles can facilitate the coexistence of competing predators.
• Food web dynamics are sensitive to boundary conditions and the presence of oscillatory behaviors.