Firefly Synchronization Dashboard

An interactive R Shiny application for exploring mathematical models of firefly synchronization.

An interactive R Shiny application for exploring mathematical models of firefly synchronization. Features four biologically-inspired models (Kuramoto oscillators, spatial coupling, integrate-and-fire, and hybrid multi-species), real-time phase space visualization, chimera state detection, critical slowing down analysis, and bifurcation diagrams. Built to investigate collective behavior and phase transitions in coupled oscillator systems.

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Quick Start Guide

  1. Select a Model from the dropdown menu
  2. Adjust Parameters using the sliders (coupling strength K, population size N, frequency spread σ)
  3. Click “Run Simulation” to execute
  4. Explore Results across three tabs:
    • Phase Space – See firefly phases on a circular plot or 2D scatter
    • Order Parameter – Track synchronization level over time
    • Raster Plot – View individual flash events (I&F and Hybrid models)
  5. Compute Bifurcation to see how synchronization changes across coupling strengths
  6. Export Data as CSV for further analysis

Model Descriptions

1. P. frontalis (Kuramoto)

Classic coupled oscillator model where each firefly adjusts its phase based on the average of all others. At low coupling, fireflies flash independently. Above the critical threshold (K_c ≈ 0.20), they spontaneously synchronize. Can exhibit chimera states—groups of synchronized and desynchronized fireflies coexisting.

2. P. frontalis (Spatial)

Extension of Kuramoto where coupling strength decays with distance. Nearby fireflies influence each other more than distant ones. Creates spatially-organized clusters and wave patterns. Controlled by coupling range parameter (r).

3. P. carolinus (Integrate-and-Fire)

Pulse-coupled model where fireflies accumulate charge and flash when reaching a threshold, then reset. When one flashes, it nudges others closer to firing. Produces characteristic synchronous bursts separated by quiet periods. Critical coupling β_c ≈ 0.13.

4. Mixed Species (Hybrid)

Combines Kuramoto and integrate-and-fire populations with cross-species coupling. Simulates mixed swarms where two species with different signaling mechanisms interact. Explore how species ratio and inter-species coupling affect collective synchronization.

Tech: R, Shiny, ggplot2, Plotly

Inspired by the research of Dr. Orit Peleg (CU Boulder) and Dr. Daniel Abrams (Northwestern).