Reservoir computing and multi-scroll attractors: How network topologies shape prediction performance

Multi-scroll attractors are complex chaotic systems with high-dimensional nonlinear dynamics, making their modeling and prediction a challenging task. While reservoir computing (RC) has been successfully applied to various chaotic time-series problems, its effectiveness in modeling multi-scroll attractors has not been explored. To the best of our knowledge, this study is the first to conduct a comprehensive investigation of RC for multi-scroll attractors, systematically analyzing the impact of nine different network topologies on predictive performance. The examined reservoir structures include lattice, scale-free, small-world, random, star, mesh, ring, star-mesh hybrid, and mesh-ring hybrid networks. To assess the effectiveness of each topology, an RC model is trained to reconstruct phase-space trajectories using the predicted time-series data from three distinct multi-scroll attractor systems. Performance is quantitatively evaluated using Largest Lyapunov Exponent (LLE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and Mean Absolute Error (MAE). Additionally, the structural properties of each network is analyzed using Frobenius norm analysis, providing insights into the relationship between network connectivity and predictive accuracy. The results demonstrate that star-mesh and mesh-ring hybrid networks achieve the lowest error values in most case, indicating superior performance in multi-scroll attractor reconstruction, while random and mesh networks exhibit higher error rates, suggesting limited predictive capability. Furthermore, Frobenius norm analysis reveals that moderate network connectivity enhances attractor reconstruction accuracy. These findings provide critical insights into optimizing RC architectures for multi-scroll attractor modeling.