Chaotic patterns in the discrete-time dynamics of social foraging swarms with attractant–repellent profiles: an analysis

Abstract

This article investigates the chaotic dynamical characteristics of a discrete-time social foraging swarm model in which the individuals move in a d-dimensional space according to an attractant/repellent or a nutrient profile. The collective behavior of the swarm model results from the balance between inter-individual interactions and the simultaneous interactions of the swarm members with their environment. Analysis undertaken in the paper indicates that chaos can be introduced into the system by tuning the parameters of the mutual attraction-repulsion function and the attractant–repellent profiles of the swarm dynamics [as given in Eq. (1)]. Ranges of different parameters to ensure sufficient condition for chaotic characteristics have been determined. Apart from chaos, stable and limit cyclic behaviors are also demonstrated for various parameter ranges. Effect of different attractant/repellent gradient profiles on the mean swarm trajectory in the presence of chaos has also been studied. Presence of chaos is determined by means of the Lyapunov exponent. Results obtained from the theoretical analysis are validated through comprehensive simulations.