Synchronized bioluminescence behavior of a set of fireflies involving fractional operators of Liouville–Caputo type

Abstract

In this paper, a system of fractional differential equations that model the synchronized bioluminescence behavior of a set of fireflies put on two spatial arrangements is presented; the alternative representation of these equations contains fractional operators of Liouville–Caputo type. The objective of the model is to qualitatively recover synchronization and show that it is persistent. It is shown that the effort made by each firefly glow changes with respect to the number of male competitors and the distance between them. The conditions on biological parameters are interpreted.