Characterization of Swarm Behavior Through Pair-Wise Interactions by Tsallis Entropy

Abstract

This paper tries to look at the interactions of a swarm of two at an elementary level. The change in the swarm entropy during the interactions is investigated. The characterization of swarm behavior has been subsumed in four modes, i.e. normal-free, normal-swarm, feeding and obstacle modes. Based on these modes, an entropy based algorithm is constructed to observe pair-wise interactions for each mode. For these modes, individuals of swarm are taken into account as self-driven interacting particles in the mathematical model. Statistical entropy definitions are used to control individual's behavior in feeding and obstacle modes. Individuals lose interactions enabling swarm behavior in feeding mode because of the priority of feeding for individuals as in nature. On the other hand, when swarm confronts an obstacle, individuals interact as much as they can. However they may lose interaction, depending on the size of the obstacle and position of the individuals. For feeding and obstacle modes, it is observed that Tsallis Entropy fits in the simulation better than other entropy definitions such as Shannon and Renyi.