On the limit of large couplings and weighted averaged dynamics

W Wiegerinck, W Burgers, FM Selten

We consider a network of deterministic non-linear oscillators with nonidentical parameters. Interactions between the di fferent oscillators are
linear, but the coupling coefficients for each interaction may diff er. We consider the case where coupling coefficients are suciently large, so that
the diff erent oscillators will have their state variables strongly tied together and variables of the di fferent oscillators will rapidly become (almost) synchronized. We will argue that the dynamics of the network is approximated by the dynamics of weighted averages of the vector fi elds
of the di fferent oscillators. Our focus of application will be on so-called supermodeling, a recently proposed model combination approach in which diff erent existing models are dynamically coupled together aiming to improved performance. With large coupling theory, we are able to analyze and better understand earlier reported supermodeling results. Furthermore, we explore the behavior in partially coupled networks, in particular supermodeling with incomplete models, each modeling a di fferent aspect of the truth. Results are illustrated numerically for the Lorenz 63 model.

Bibliographic data

W Wiegerinck, W Burgers, FM Selten. On the limit of large couplings and weighted averaged dynamics
Year: 2013

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