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

Maciej Leszczynski, Przemyslaw Perlikowski and Piotr Brzeski ()
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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

Mathematics, 2024, vol. 12, issue 7, 1-19

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.

Keywords: sampled-based methods; detection of solutions; basin stability; basin entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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