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Abstract: Inferring network topology from dynamical observations is a fundamentalproblem pervading research on complex systems. Here, we present a simple,direct method to infer the structural connection topology of a network, givenan observation of one collective dynamical trajectory. The general theoreticalframework is applicable to arbitrary network dynamical systems described byordinary differential equations. No interference external driving is requiredand the type of dynamics is not restricted in any way. In particular, theobserved dynamics may be arbitrarily complex; stationary, invariant ortransient; synchronous or asynchronous and chaotic or periodic. Presupposing aknowledge of the functional form of the dynamical units and of the couplingfunctions between them, we present an analytical solution to the inverseproblem of finding the network topology. Robust reconstruction is achieved inany sufficiently long generic observation of the system. We extend our methodto simultaneously reconstruct both the entire network topology and allparameters appearing linear in the system-s equations of motion. Reconstructionof network topology and system parameters is viable even in the presence ofsubstantial external noise.

Autor: Srinivas Gorur Shandilya, Marc Timme



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