Spatial Dynamics of a Leslie-Gower Type Predator-Prey Model with Interval Parameters

Due to various imprecisions in nature, imprecise parameters in biological modeling should be taken into account. This paper studies the spatial dynamics of an imprecise prey-predator model of the Leslie-Gower type by presenting imprecise parameters as interval parameters. First, conditions of Turing instability are obtained via bifurcation analysis and interval-valued functions. Then, the effects of interval parameters on pattern selection are discussed via multiple-scale analysis. We discover that when all the parameters of the model are interval parameters, the value of the controlled parameter increases, and the range of the pattern selection domain expands as the value of the interval variable increases, i.e., both the controlled parameter and boundary of the pattern selection domain are interval numbers. Finally, under the effects of the interval parameters of diffusion and the prey's conversion rate into biomass for the predator, the density of the prey decreases or increases, respectively, and the structure or the microstructure of the pattern of the model changes with the growing value of the interval variable. This paper provides a new perspective on the study of the spatial predator-prey model.