Analysis of the Dynamics of the Echo State Network Model Using Recurrence Plot

  • Emmanuel Sam
  • Sebastian Basterrech
  • Pavel KromerEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 874)


At the beginning of the 2000s, a specific type of Recurrent Neural Networks (RNNs) was developed with the name Echo State Network (ESN). The model has become popular during the last 15 years in the area of temporal learning. The model has a RNN (named reservoir) that projects an input sequence in a feature map. The reservoir has two main parameters that impact the accuracy of the model: the reservoir size (number of neurons in the RNN) and the spectral radius of the hidden-hidden recurrent weight matrix. In this article, we analyze the impact of these parameters using the Recurrence Plot technique, which is a useful tool for visualizing chaotic systems. Experiments carried out with three well-known dynamical systems show the relevance of the spectral radius in the reservoir projections.


Recurrent Neural Network Echo State Network Recurrence Plot Chaotic systems Time-series problems 



This work was supported by the Czech Science Foundation under the grant no. GJ16-25694Y, and by the projects SP2018/126 and SP2018/130 of the Student Grant System, VSB-Technical University of Ostrava, and it has been supported by the Czech Science Foundation (GAČR) under research project No. 18-18858S.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Emmanuel Sam
    • 1
  • Sebastian Basterrech
    • 2
  • Pavel Kromer
    • 3
    Email author
  1. 1.Nduom School of Business and TechnologyElminaGhana
  2. 2.Department of Computer Science, Faculty of Electrical EngineeringCzech Technical UniversityPragueCzech Republic
  3. 3.Faculty of Electrical Engineering and Computer ScienceVŠB-Technical University of OstravaOstravaCzech Republic

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