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Wada index based on the weighted and truncated Shannon entropy

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Abstract

The Wada index based on the weighted and truncated Shannon entropy is presented in this paper. The proposed Wada index can detect if a given basin boundary is a Wada boundary. Moreover, the Wada index does represent the number and the distribution of different colors (attractors) in the two-dimensional phase space of initial conditions. The Wada index is based on the standard box counting algorithm, but computations in each box are based on the weighted and truncated Shannon entropy. That makes the algorithm for the computation of the Wada index conveniently applicable for different basins of attraction represented as color digital images. Computational experiments are used to demonstrate the advantages of the proposed index and compare it with other existing techniques and algorithms for the numerical analysis of Wada boundaries.

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Acknowledgements

Financial support from the Key Project of Natural Science Foundation of China (No. 61833005), the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Projects No. FIS2016-76883-P and No. PID2019-105554GB-I00 is acknowledged. The research was also supported by the Research and Innovation Fund of Kaunas University of Technology (No. PP59/2011).

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Authors and Affiliations

  1. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-140, 51368, Kaunas, Lithuania

    Loreta Saunoriene

  2. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-146, 51368, Kaunas, Lithuania

    Minvydas Ragulskis

  3. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  4. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuán

  5. Department of Applied Informatics, Kaunas University of Technology, Studentu 50-415, 51368, Kaunas, Lithuania

    Miguel A. F. Sanjuán

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  1. Loreta Saunoriene
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  2. Minvydas Ragulskis
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  3. Jinde Cao
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  4. Miguel A. F. Sanjuán
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Correspondence to Minvydas Ragulskis.

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Saunoriene, L., Ragulskis, M., Cao, J. et al. Wada index based on the weighted and truncated Shannon entropy. Nonlinear Dyn 104, 739–751 (2021). https://doi.org/10.1007/s11071-021-06261-1

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