Closed Theory for Nested Hyperedge Kuramoto Dynamics

Analytical framework for synchronization onset and bistability on regular hypergraphs with tunable inter-order nestedness parameter alpha.

33.3%
Onset Reduction (alpha=1)
sigma1*: 1.0 to 0.667
12.5%
Bistability Increase
hat_sigma2: 1.0 to 1.125
N=200
Simulation Nodes
k1=10, k2=5
0.5
Lorentzian Width (gamma)
sigma2 = 3.0

Synchronization Onset vs Nestedness

sigma1*(alpha) = 2*gamma - alpha*sigma2*2k2/[k1(k1-1)]

Bistability Threshold vs Nestedness

hat_sigma2(alpha) = 2*gamma / [1 - alpha*2k2/(k1(k1-1))]

Interactive: Onset and Bistability vs Parameters

0.5 3.0

Robustness Across Degree Configurations

Degree Configuration Details

(k1, k2)Onset alpha=0Onset alpha=1Reduction %Bistab Increase %
(6, 3)1.0000.40060.0%25.0%
(10, 5)1.0000.66733.3%12.5%
(15, 8)1.0000.77122.9%8.3%
(20, 10)1.0000.84215.8%5.6%