2021/11/24 by Muhittin Cenk Eser, Eser, Muhittin Cenk, Mustafa Riza +1
Computer Science · #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2111.12753
We study interlayer synchronisation in a duplex network of N=300 nonlocally coupled Kuramoto--Sakaguchi oscillators, with each layer operating in the chimera regime. The interlayer coupling is weak (σ12=0.01), sparse, and time-varying: a fixed number NIL of replica-node pairs are coupled symmetrically, and the active links are randomly redistributed every Tswt time units. We characterise synchronisation by the time-averaged interlayer order parameter Z, the master stability function Ψ(σ12,Tswt), and the finite-time transverse Lyapunov exponent λ_⊥. In the static case, full synchronisation (Z=1, Ψ<0) requires all-to-all interlayer coupling (NIL=N). Under temporal switching with Tswt≤ 25, near-complete synchronisation is achieved with as few as NIL≈ N/3 links, while the intralayer chimera structure is preserved. The master stability function confirms that short switching periods render the transverse dynamics stable at link densities where static coupling fails, and the transverse Lyapunov exponent heatmap delineates the critical link number as a joint function of NIL and Tswt. These results demonstrate that temporal redistribution of sparse interlayer connections can stabilise replica-node coherence in networks with spatially heterogeneous intralayer dynamics.