Stochastic differential equation models on sphere for animal migration

Abstract

Animal migration is a seasonal movement of a bundle of animals from place to place. A migration cycle is often annually and closely linked with the cyclic pattern of seasons. A short-distance migration can be modeled on a planar surface, but most animals have long-distance migrations, e.g., Arctic terns migrate from the North Pole to the South Pole; thus, their migration should be modeled on a spherical surface. In addition, the Brownian motion term is included in a model to represent noises and randomness of movements. This work aims to simulate their migration routes using stochastic differential equations (SDEs) on sphere together with additional behavior functions describing behaviors of animals during their migration. The models are constructed based on SDEs on planar surface whose solution moves toward a particular point which is then transformed to SDEs on sphere using appropriate map projection functions. Finally, the simulations of routes are constructed using the Euler-Maruyama scheme to show animal migration routes.