Abstract
Synchronization in pulse-coupled oscillators has been broadly studied under different perspectives. We present a game with simple rules to describe synchronization in such kinds of oscillators. This game, intended to describe easily how fireflies synchronize, constitutes a discrete model different from those based on maps, ordinary differential equations, or multi-agent systems. Our results on complete synchronization depend strongly on the used rules that we compare statistically. We also calculate the basins of attraction to quantify the importance of the initial conditions in reaching or not synchronization and the time intervals required for that.
Highlights
Synchronization is one of the most common phenomena occurring in oscillating systems in nature and in man-made systems; it inheres to the adjustment of self-sustained oscillators rhythms [1]
We consider the following four complementary variants of Rule 4, named nr: (a) When a firefly is in a box located on the last side of the polygon, it might overtake the flashing box without flashing in its cycle. This fact imposes a difficulty in attaining complete synchronization
We remark that the computation of the basins of attraction is related to the elapsed time to achieve complete synchronization with simultaneous collective flashing
Summary
Synchronization is one of the most common phenomena occurring in oscillating systems in nature and in man-made systems; it inheres to the adjustment of self-sustained oscillators rhythms [1]. The goal of the game is for all fireflies to flash synchronously and simultaneously in the shortest possible time, given a specific set of initial conditions.
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