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A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

Author

Listed:
  • Maciej Leszczynski

    (Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland)

  • Przemyslaw Perlikowski

    (Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland)

  • Piotr Brzeski

    (Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland)

Abstract

This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems.

Suggested Citation

  • Maciej Leszczynski & Przemyslaw Perlikowski & Piotr Brzeski, 2024. "A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method," Mathematics, MDPI, vol. 12(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:987-:d:1364283
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    References listed on IDEAS

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    1. Zoran Benic & Petar Piljek & Denis Kotarski, 2016. "Mathematical modelling of unmanned aerial vehicles with four rotors," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 14(1), pages 88-100.
    2. Wade, M.J. & Harmand, J. & Benyahia, B. & Bouchez, T. & Chaillou, S. & Cloez, B. & Godon, J.-J. & Moussa Boudjemaa, B. & Rapaport, A. & Sari, T. & Arditi, R. & Lobry, C., 2016. "Perspectives in mathematical modelling for microbial ecology," Ecological Modelling, Elsevier, vol. 321(C), pages 64-74.
    3. Naik, Manisha Krishna & Baishya, Chandrali & Veeresha, P., 2023. "A chaos control strategy for the fractional 3D Lotka–Volterra like attractor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 1-22.
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