Entrainment and synchronization in networks of Rayleigh-van der Pol oscillators with diffusive and Haken-Kelso-Bunz couplings.
We analyze a network of non-identical Rayleigh-van der Pol (RvdP) oscillators interconnected through either diffusive or nonlinear coupling functions. The work presented here extends existing results on the case of two nonlinearly coupled RvdP oscillators to the problem of considering a network of three or more of them. Specifically, we study synchronization and entrainment in networks of heterogeneous RvdP oscillators and contrast the effects of diffusive linear coupling strategies with the nonlinear Haken-Kelso-Bunz coupling, originally introduced to study human bimanual experiments. We show how convergence of the error among the nodes' trajectories toward a bounded region is possible with both linear and nonlinear coupling functions. Under the assumption that the network is connected, simple, and undirected, analytical results are obtained to prove boundedness of the error when the oscillators are coupled diffusively. All results are illustrated by way of numerical examples and compared with the experimental findings available in the literature on synchronization of people rocking chairs, confirming the effectiveness of the model we propose to capture some of the features of human group synchronization observed experimentally in the previous literature.
Department of Engineering Mathematics, Merchant Venturers' Building, University of Bristol, Woodland Road, Clifton, Bristol, BS8 1UB, UK.
Francesco
F
Alderisio
EuroMov, Montpellier University, 700 Avenue du Pic Saint-Loup, 34090, Montpellier, France.|Institut Universitaire de France, 1 rue Descartes, 75231, Paris Cedex 05, France.
Benoît G
BG
Bardy
Department of Engineering Mathematics, Merchant Venturers' Building, University of Bristol, Woodland Road, Clifton, Bristol, BS8 1UB, UK. m.dibernardo@bristol.ac.uk.|Department of Electrical Engineering and Information Technology, University of Naples Federico II, Via Claudio 21, 80125, Naples, Italy. m.dibernardo@bristol.ac.uk.
Mario
M
di Bernardo
D003198:Computer Simulation; D003491:Cybernetics; D004058:Diffusion; D006801:Humans; D017711:Nonlinear Dynamics; D013997:Time Factors
Entrainment; Group synchronization; HKB coupling; Heterogeneous networks; Human coordination; Nonlinear oscillators