An unified approach for the calculation of different sample-based measures with single sampling method

Abstract

This paper investigates two sample-based methods for analysing multistable systems, i.e., basin stability and basin entropy. Both methods are based on the large number of numerical integration trials obtained for a large set of different initial conditions. The obtained data is classified and used to determine measures that describe the stability of solutions, the structure of the phase space and the predictability of system dynamics. The basin stability reflects the overall probability of reaching given solutions, and the basin entropy measure was proposed to reflect the structure of basins of attraction and the complexity of their boundaries. While these two measures complement one another finely, the procedures originally proposed to obtain them differ significantly. The paper proposes a universal approach and algorithm to obtain the value of basin stability and basin entropy measures. The applicability of the proposed procedures is presented for two nonlinear systems.