A stochastic predator-prey model with two competitive preys and Ornstein-Uhlenbeck process

Area of Science:

• Mathematical Biology
• Stochastic Differential Equations
• Ecology

Background:

• Predator-prey models are fundamental in ecology.
• Stochasticity is crucial for realistic population dynamics.
• Understanding competitive interactions enhances ecological models.

Purpose of the Study:

• To formulate and analyze a stochastic predator-prey model with two competitive prey.
• To investigate the population dynamics, including boundedness and stability.
• To establish conditions for the existence of a stationary distribution.

Main Methods:

• Formulation of a stochastic differential equation model.
• Analysis of unique global solutions and pth moment boundedness.
• Application of stochastic Lyapunov functions for stability analysis.
• Derivation of covariance matrix near equilibrium.

Main Results:

• The stochastic system possesses a unique global solution.
• Asymptotic pathwise estimations of the population dynamics were performed.
• Sufficient conditions for the existence of a stationary distribution were derived.
• The covariance matrix near quasi-positive equilibrium was determined.

Conclusions:

• The study provides a comprehensive analysis of a complex stochastic predator-prey system.
• Theoretical findings are validated through numerical simulations.
• The research contributes to a deeper understanding of ecological population dynamics under stochastic influences.