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Efficient Parameter Search for Chaotic Dynamical Systems Using Lyapunov-Based Reinforcement Learning
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DOI：10.3390/sym17111832.png)
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This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the H & eacute;non map, the Lorenz system, Chua's circuit, the Lorenz-Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used as a scalar reward to guide exploration toward regions with high sensitivity to initial conditions. Under matched evaluation budgets, the approach reduces redundant simulations relative to grid scans and accelerates discovery of parameter sets with large positive LLE. Experiments report learning curves, parameter heatmaps, and representative phase portraits that are consistent with Lyapunov-based assessments. Q-learning typically reaches high-reward regions earlier, whereas SARSA shows smoother improvements over iterations. Several evaluated systems possess equation-level symmetry-most notably sign-reversal invariance in the Lorenz system and Chua's circuit models and a coordinate-wise sign pattern in the Lorenz-Haken equations-which manifests as mirror attractors and paired high-reward regions; one representative is reported for each symmetric pair. Overall, Lyapunov-guided reinforcement learning serves as a practical complement to grid and random search for chaos identification in both discrete maps and continuous flows, and transfers with minimal changes to higher-dimensional settings. The framework provides an efficient method for identifying high-complexity parameters for applications in chaos-based cryptography and for assessing stability boundaries in engineering design.
Keyword:
chaotic systems
Lyapunov exponent
parameter exploration
reinforcement learning
Q-learning
SARSA
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2.2
论文数:
1.4K
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