Sep 2026· Zenodo (CERN European Organization for Nuclear Research)
Chaos control and synchronization
Abstract
The study of complex systems often faces challenges in characterizing their inherent dynamics and identifying emergent patterns. Traditional chaos theory metrics, while valuable, often fail to fully capture the nuanced interplay of non-linear interactions driving these patterns. This paper introduces the Dynamical Chaos Metric Alignment (DCMA), a novel metric system designed to quantify "dynamical chaos" – the instability and adaptability of complex systems – through a dynamic, adaptive weighting mechanism. The DCMA leverages Lyapunov exponent analysis, enhanced by a novel weighting function that explicitly models the system's historical trajectory, offering a more robust and insightful approach to quantifying and aligning chaotic behavior. We demonstrate the DCMA's effectiveness through a series of illustrative examples across diverse systems, including fluid dynamics, neural networks, and protein folding, showcasing its ability to identify and quantify key characteristics of dynamical chaos. The research explores the potential for the DCMA to contribute to a deeper understanding of complex systems and inform the design of robust and adaptable control strategies.
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