Study of a 2 dimensional aggregation model with non-linear adaptations

Abstract

In this paper we will explore the impacts on collective animal motion of adding non-linearity to the animals’ turning rate in a 2-dimensional model of aggregation. The model in question was proposed by Fetecau and implements a dependence on an individual’s relation to neighbours’ position and the direction in which they are moving. By utilizing a turning rate formula similar to one proposed by Eftimie, we can retain many of the dependences of the original 2-dimensional model while ensuring that the turning rate is both bounded and non-linear. The group formations resulting from this introduction of non-linearity are explored.