On Lagrangian dynamics based modeling of swarm behavior

In this article a Lagrangian dynamics based approach for modeling swarm dynamics is presented. The approach is based on energy and is alternative to the commonly used Newtonian dynamics, which is based on forces. For that purpose first the concept of biological potential energy is introduced. Various components of the biological potential energy such as swarming potential energy, environmental potential energy, and predator potential energy are also introduced and example kernel functions discussed. Simple illustrative numerical simulations are also provided.