A nonlinear and nonlocal model for animal aggregation

Abstract

An aggregation model is a kind of model used to show the dynamics of the distribution of the population of organisms. Mathematically, we can use a partial differential equation to model the density of an organism at different times and locations. In this paper, we are going to look at a 2+1-dimensional nonlinear and nonlocal aggregation model proposed by Fetecau [8] with an adaptation of a saturation function to the nonlinear term. The nonlinear term represents the interaction between an individual and its neighbours. The saturation function can suppress or amplify the interaction at a low or high level depending on the values of some parameters in the saturation function. We will explore the behaviour of the model with different saturation functions applied.