
A Distributed Algorithm for Computing a Common Fixed Point of a Finite Family of Paracontractions
A distributed algorithm is described for finding a common fixed point of...
03/15/2017 ∙ by Daniel Fullmer, et al. ∙ 0 ∙ shareread it

Cognition in Dynamical Systems, Second Edition
Cognition is the process of knowing. As carried out by a dynamical syste...
04/09/2018 ∙ by Jack Hall, et al. ∙ 0 ∙ shareread it

'Almost Sure' Chaotic Properties of Machine Learning Methods
It has been demonstrated earlier that universal computation is 'almost s...
07/28/2014 ∙ by Nabarun Mondal, et al. ∙ 0 ∙ shareread it

Herding as a Learning System with EdgeofChaos Dynamics
Herding defines a deterministic dynamical system at the edge of chaos. I...
02/09/2016 ∙ by Yutian Chen, et al. ∙ 0 ∙ shareread it

Numerical schemes to reconstruct three dimensional timedependent point sources of acoustic waves
This paper is concerned with the numerical simulation of the three dimen...
06/22/2019 ∙ by Bo Chen, et al. ∙ 0 ∙ shareread it

On the Relation of Impulse Propagation to Synaptic Strength
In neural network, synaptic strength could be seen as probability to tra...
05/23/2018 ∙ by Lan Sizhong, et al. ∙ 0 ∙ shareread it

Bargaining for Revenue Shares on Tree Trading Networks
We study trade networks with a tree structure, where a seller with a sin...
04/22/2013 ∙ by Arpita Ghosh, et al. ∙ 0 ∙ shareread it
Datadriven Reconstruction of Nonlinear Dynamics from Sparse Observation
We present a datadriven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the universal function approximation capability of ESN, it is shown that the reconstruction problem can be formulated as a fixedpoint problem, in which the trajectory of the dynamical system is a fixed point of the ESN. An underrelaxed fixedpoint iteration is proposed to reconstruct the nonlinear dynamics from a sparse observation. The proposed fixedpoint ESN is tested against both univariate and multivariate chaotic dynamical systems by randomly removing up to 95 reconstruct the complex dynamics from only 5 10 relatively simple nonchaotic dynamical system, the numerical experiments on a forced van der Pol oscillator show that it is possible to reconstruct the nonlinear dynamics from only 1 2
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