Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technical University of Dresden, 01062, Dresden, Germany.
Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Goettingen, Germany.
Nat Commun. 2017 Dec 19;8(1):2192. doi: 10.1038/s41467-017-02288-4.
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.
网络动力系统中的相互作用拓扑结构从根本上决定了它们的功能。加速技术进步创造了大量关于物理、生物和技术系统中集体非线性动力学的数据。然而，从这些动力学中检测直接相互作用模式仍然是一个主要的开放问题。特别是，目前的非线性动力学方法大多需要事先知道（通常是高维）系统动力学的模型。在这里，我们开发了一种无需模型的框架，仅从记录生成的非线性集体动力学中推断直接相互作用。通过引入显式依赖矩阵并结合块正交回归算法，该方法在许多动力学状态下都能可靠地工作，包括稳态的瞬态动力学、周期性和非周期性动力学以及混沌。该框架还可以揭示网络（两点）和超网络（例如，三点）相互作用，因此可以在没有模型的情况下，为推断不同系统中的直接相互作用模式提供非线性动力学选择。
