Binary interaction algorithms for the simulation of flocking and swarming dynamics

TL;DR

This paper introduces efficient binary interaction algorithms for simulating large flocking and swarming systems, reducing computational complexity from quadratic to linear through stochastic methods based on kinetic equations.

Contribution

The paper presents a novel stochastic simulation approach using binary interactions and kinetic equations to efficiently model large-scale flocking and swarming dynamics.

Findings

Algorithms significantly reduce computational costs

Numerical results demonstrate high efficiency

Approach accurately approximates large flocking systems

Abstract

Microscopic models of flocking and swarming takes in account large numbers of interacting individ- uals. Numerical resolution of large flocks implies huge computational costs. Typically for $N$ interacting individuals we have a cost of $O(N^2)$. We tackle the problem numerically by considering approximated binary interaction dynamics described by kinetic equations and simulating such equations by suitable stochastic methods. This approach permits to compute approximate solutions as functions of a small scaling parameter $\varepsilon$ at a reduced complexity of O(N) operations. Several numerical results show the efficiency of the algorithms proposed.