bSTAB: an open-source software for computing the basin stability of multi-stable dynamical systems

Abstract

The pervasiveness of multi-stability in nonlinear dynamical systems calls for novel concepts of stability and a consistent quantification of long-term behavior. The basin stability is a global stability metric that builds on estimating the basin of attraction volumes by Monte Carlo sampling. The computation involves extensive numerical time integrations, attractor characterization, and clustering of trajectories. We introduce , an open-source software project that aims at enabling researchers to efficiently compute the basin stability of their dynamical systems with minimal efforts and in a highly automated manner. The source code, available at https://github.com/TUHH-DYN/bSTAB/, is available for the programming language featuring parallelization for distributed computing, automated sensitivity and bifurcation analysis as well as plotting functionalities. We illustrate the versatility and robustness of for four canonical dynamical systems from several fields of nonlinear dynamics featuring periodic and chaotic dynamics, complicated multi-stability, non-smooth dynamics, and fractal basins of attraction. The projects aims at fostering interdisciplinary scientific collaborations in the field of nonlinear dynamics and is driven by the interaction and contribution of the community to the software package.

Nuancing Stability for Self-Sustained Musical Instruments: Transient Durations and Basins of Attraction

“…However, this method is meant to be applied on more complex systems for which basins of attraction might be unknown. Usually, a criteria based on a time integration is used [15]. In that respect, we have chosen that type of criteria to test our method.…”

Nonlinear Feedback Synthesis and Control of Periodic, Quasiperiodic, Chaotic and Hyper-Chaotic Oscillations in Mechanical Systems

“…3(a) that the system may exhibit periodic, intermittency [60] and chaotic responses. The approximate relative basin volumes of initial conditions in the y y − plane computed using bSTAB toolbox of MATLAB [57] are shown in Fig. 3…”

“…Based on the analysis and numerical simulations, different regions of control gains are delineated for different types of responses. The Basins of attraction of the responses are plotted using the bSTAB toolbox of MATLAB [57]. Bifurcations of system response and approximate relative basin volume of initial conditions with controller parameters are also plotted.…”

Preface to the special issue NODYCON 2021, Second International Nonlinear Dynamics Conference, Feb. 16–19, 2021

“…The first topical area titled Concepts and methods in nonlinear dynamics includes articles concerning the computation of invariant manifolds in high-dimensional finite element models [ 1 ], the computation of the basins of attraction of multi-stable dynamical systems [ 2 ], reduced-order models for vertical sloshing employing neural networks [ 3 ], the problem of continuous representations of piecewise-smooth nonlinear systems [ 4 ], and analytical approaches to nonlinear singular traveling waves in compressible thermo-hyperelastic cylindrical shells [ 5 ].…”