PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Synchronisation, cascades and the resilience of networks
Problem
A population of N=500 field crickets chirps in a meadow. Each cricket can hear roughly c=5 neighbours well enough to adjust its chirp phase to theirs, modelled as an Erdos-Renyi network of that mean degree. Chirp rates scatter about a common value with a Lorentzian half-width Δ=0.80rads−1 (reflecting temperature variation across the meadow, since chirp rate is temperature-dependent). Laboratory measurements of paired crickets give an effective phase coupling K=0.50rads−1.
((a)) Estimate κ1 for the hearing network.
((b)) Estimate the synchronisation threshold Kc on this network.
((c)) Determine whether the measured coupling is sufficient for the chorus to synchronise, and by what factor it exceeds or falls short of the estimated threshold.