Sensitivity analysis and stationary probability distributions of a stochastic two-prey one-predator model

Abstract

In this paper, we perform sensitivity analysis to a stochastic two-prey one-predator model and investigate the stationary probability distributions of its population densities. The semi-relative and logarithmic sensitivity functions are utilized to evaluate the effects of system parameters on the population of each species, and to conduct the uncertainty quantification of the model. By numerically solving the Fokker–Planck–Kolmogorov (FPK) equation of the stochastic predator–prey model, we acquire the influence mechanism of various system parameters on population densities under environmental disturbances. In addition, we discuss the nonessential parameters in the system, which can be weakened or modified to simplify the model. Finally, the consistency of the numerical solutions and the Monte Carlo simulation results shows that the stochastic response solutions of the three-species system based on the splitting method and the chasing method are reliable.