Outer Synchronization of Simple Firefly Discrete Models in Coupled Networks

Abstract

Synchronization is one of the most important emerging collective behaviors in nature, which results from the interaction in groups of organisms. In this paper, network synchronization of discrete-time dynamical systems is studied. In particular, network synchronization with fireflies oscillators like nodes is achieved by using complex systems theory. Different cases of interest on network synchronization are studied, including for a large number of fireflies oscillators; we consider synchronization in small-world networks and outer synchronization among different coupled networks topologies; for all presented cases, we provide appropriate ranges of values for coupling strength and extensive numerical simulations are included. In addition, for illustrative purposes, we show the effectiveness of network synchronization by means of experimental implementation of coupled nine electronics fireflies in different topologies.

The Emergence of Hyperchaos and Synchronization in Networks with Discrete Periodic Oscillators

“…Dynamical networks with discrete periodic oscillators are constructed, which in a simple way, may represent organisms interacting with each other, for example fireflies [18]. Figure 1 illustrates a simple network with two bidirectionally-coupled discrete periodic nodes.…”

“…Recently, we have studied the coupling of periodic oscillators, as a very simple model of fireflies on nearest-neighbor, star and small-world topologies [18]. This allows understanding some important aspects of behavior, interaction, coupling and synchronization of simple models that can represent living organisms with common goals and collective behavior.…”

The Wonder World of Complex Systems

“…Using the electronic circuit shown in Figure 5, cf. (Arellano-Delgado et al 2015), it is possible to electronically reproduce the behavior of a firefly. And in turn, it is possible to mimic the synchronization of these insects without having to enter their reproductive habitats.…”

Testing a Firefly-Inspired Synchronization Algorithm in a Complex Wireless Sensor Network

“…Because firefly-inspired synchronization is not compatible with most commercially available WSN chips [20], very few groups have used firefly-inspired synchronization. Some groups have adopted firefly-inspired synchronization on special platforms such as a Wire [21,22], Ultra Wideband (UWB) [23], Custom Radio [24] and Light Emitting Diode (LED) [25]. …”