Abstract

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Highlights

  • The topology of interactions in network dynamical systems fundamentally underlies their function

  • Current nonlinear dynamics approaches may recover direct interactions from the collective dynamics of a system if a mathematical model is provided in advance and only their unknown parameters, network links, and nonlinear terms are to be determined[11,12,13,14,15,16,17,18,19]

  • We propose a novel concept for inferring direct interactions in coupled dynamical systems, relying only on their nonlinear collective dynamics, with neither assuming specific dynamic models to be known in advance nor assuming the dynamics admits a sparse representation, nor imposing controlled drivings, nor expecting statistical dependencies to faithfully reveal direct, physical interactions

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Summary

Introduction

The topology of interactions in network dynamical systems fundamentally underlies their function. We propose a novel concept for inferring direct interactions in coupled dynamical systems, relying only on their nonlinear collective dynamics, with neither assuming specific dynamic models to be known in advance nor assuming the dynamics admits a sparse representation, nor imposing controlled drivings, nor expecting statistical dependencies to faithfully reveal direct, physical interactions. To achieve this goal, we here change the perspective and ask which units j of the network provide direct physical interactions to a given unit i and appear on the right hand side of its differential equation, rather than asking for details of the interaction functions among those units. Interaction networks may even be revealed if some units are not measured (and hidden during observation)

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