Deep Learning-based Analysis of Basins of Attraction

TL;DR

This paper demonstrates that convolutional neural networks can efficiently analyze and characterize basins of attraction in dynamical systems, outperforming traditional computational methods and enabling better understanding of complex system behaviors.

Contribution

The study introduces a novel CNN-based approach for basin analysis, showing its superior performance over conventional methods in dynamical systems characterization.

Findings

CNNs outperform traditional methods in basin analysis

Proposed approach reduces computational demand

Effective in exploring diverse dynamical behaviors

Abstract

This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field. Conventional methods become computationally demanding when analyzing multiple basins of attraction across different parameters of dynamical systems. Our research presents an innovative approach that employs CNN architectures for this purpose, showcasing their superior performance in comparison to conventional methods. We conduct a comparative analysis of various CNN models, highlighting the effectiveness of our proposed characterization method while acknowledging the validity of prior approaches. The findings not only showcase the potential of CNNs but also emphasize their significance in advancing the exploration of diverse behaviors within dynamical systems.