Application of chaos measures to a simplified boids flocking model

Abstract

Swarm intelligence systems are characterised by the emergence of structure without explicit external control, the coexistence of many stable states and the existence of state transitions with significant change of the system dynamics. Despite these characteristics being shared with the dynamics of chaotic systems, little is known of the potential relationship between swarm and chaotic systems. If indeed there is a relationship between the two, it may be possible to complement the current subjective and quantitative measures used for identifying swarming dynamics with the objective measures used in chaotic systems. This study shows that a simplified version of the original Reynolds’ ‘boids’ (short for ‘birdoid’) model and two degraded versions of the simplified model display flocking dynamics based on current measures of group and order. The simplified version of the original boids model and one of the degraded forms also show chaotic dynamics using three proposed measures of information flow, complexity and sensitivity to initial conditions. A novel $$\hbox {Chaos}_\mathrm{composite}$$ measure is introduced which combines all three measures into a single measure and shows promise for characterising flocking dynamics and potentially swarming dynamics. The measures proposed in this study, therefore, may have potential for predicting and controlling the behaviour of swarm intelligence systems.