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Model reduction of dynamical systems with a novel data-driven approach: The RC-HAVOK algorithm.

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This study explores reservoir computing (RC) for modeling complex multi-scroll attractors. Hybrid star-mesh and mesh-ring networks showed the best performance in reconstructing chaotic dynamics.

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Area of Science:

  • Nonlinear Dynamics
  • Computational Neuroscience
  • Complex Systems

Background:

  • Multi-scroll attractors exhibit high-dimensional nonlinear dynamics, posing significant modeling challenges.
  • Reservoir computing (RC) is a powerful tool for chaotic time-series prediction but its application to multi-scroll attractors remains unexplored.

Purpose of the Study:

  • To investigate the effectiveness of reservoir computing for modeling multi-scroll attractors.
  • To systematically analyze the impact of nine different network topologies on RC's predictive performance for these systems.

Main Methods:

  • Trained RC models to reconstruct phase-space trajectories of three multi-scroll attractor systems.
  • Evaluated performance using Largest Lyapunov Exponent (LLE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and Mean Absolute Error (MAE).
  • Analyzed network structural properties using Frobenius norm to correlate connectivity with accuracy.

Main Results:

  • Star-mesh and mesh-ring hybrid networks demonstrated superior performance with the lowest error rates in multi-scroll attractor reconstruction.
  • Random and mesh networks showed higher error rates, indicating limited predictive capabilities.
  • Frobenius norm analysis revealed that moderate network connectivity optimizes attractor reconstruction accuracy.

Conclusions:

  • Hybrid network topologies (star-mesh, mesh-ring) are highly effective for multi-scroll attractor modeling using reservoir computing.
  • Network connectivity plays a crucial role in the predictive accuracy of RC models for chaotic systems.
  • Findings offer insights for optimizing RC architectures for complex nonlinear dynamics.