Calculating Basins of Attraction Using CUDA: High-Resolution Mapping of Multistable Dynamics

Plotting basins of attraction reveals the global behavior of nonlinear dynamical systems, specifically in the case of multistability when multiple attractors coexist for a fixed set of parameters. However, calculation of high-resolution diagrams of attraction basins is computationally demanding due to the need for extensive numerical simulation across a large grid of initial conditions. To address this problem, we present a novel GPU-accelerated framework for efficient and scalable computation of basins of attraction using the CUDA toolkit. Our approach combines parallelized trajectory calculation with a robust feature-based clustering strategy that leverages mean peak amplitudes and mean inter-peak intervals with evaluation of fixed-point, unbound, and oscillatory regimes. In addition, we introduce an augmented data representation preserving full distributions of dynamical features, enabling subsequent analysis and parameter adjustment without additional simulation. The proposed method is validated across a diverse set of multistable systems, including cases of finite multistability, megastability, Matryoshka multistability, and extreme multistability. All designed software and obtained data have been published in public repositories to support reproducibility of the study.