Swarm interaction in 2D

Abstract

In the present work is described a simple minimal model set of ordinary differential system of equations for simulating the swarming behavior of preys under action of predators. Preys and predators are represented by a set of ODEs taking in account the Newtonian attraction-repulsion forces. The predators interacts with the preys through a Newtonian force, which is a nonconservative force (includes friction) that acts in the same direction for both agents. A perturbing force is introduced for the predators’ dynamics in order to simulate its behavior among preys. The resulting system of ordinary differential equations is solved numerically by means of Runge-Kutta of fourth order and the dynamics are discussed in the present work as the swarm’s ability to realistically avoid the predator. The main goal is to reproduce swarm behavior that has been observed in nature with the minimal and simple possible model of ODE system.