Chaotic Dynamics in Bitcoin Money Laundering: A Recurrence Quantification Analysis

Year 2026, Volume: 8 Issue: 1 , 56 - 65 , 28.03.2026

Eyyüp Ensari Şahin

https://doi.org/10.51537/chaos.1880488

https://izlik.org/JA73RR96TW

Abstract

Money laundering in cryptocurrency networks poses persistent challenges for financial intelligence units due to the pseudo-anonymous architecture of blockchain systems and the limited effectiveness of conventional rule-based detection methods. This study introduces chaos theory and recurrence quantification analysis (RQA) as a novel framework for characterizing temporal behavioral dynamics in Bitcoin money laundering transactions. Analyzing 46,564 labeled transactions from the Elliptic Bitcoin Dataset spanning 2009-2018, we construct aggregate time series for illicit and licit transaction volumes across 49 discrete temporal steps, corresponding to the dataset’s inherent graph-based snapshot structure, and apply phase space reconstruction techniques to compute three RQA metrics: determinism (DET), laminarity (LAM), and entropy (ENTR). Results reveal paradoxically higher determinism in illicit transactions (38.24% vs. 16.67% for licit), substantially elevated laminarity (35.80% vs. 0.00%), and greater entropy (0.45 vs. 0.00%), indicating that sophisticated obfuscation strategies inadvertently introduce detectable deterministic signatures. Augmenting conventional graph-based features with RQA metrics significantly enhances Random Forest classification performance, reaching near-optimal levels (F1 = 1.000, AUC = 1.000) within the evaluated dataset environment, with entropy emerging as the single most discriminative predictor. While these exceptional results reflect the high fidelity of chaos-based features in capturing structured laundering patterns from this period, they serve as a benchmark for the theoretical potential of nonlinear analysis in blockchain forensics. These findings demonstrate that temporal complexity features offer a powerful diagnostic tool for real-time monitoring and detection of systemic financial crime in evolving cryptocurrency ecosystems.

Keywords

Recurrence quantification analysis , Blockchain forensics , Chaos theory , Explainable artificial intelligence.

References

• Adadi, A. and M. Berrada, 2018 Peeking inside the black-box: A survey on explainable artificial intelligence (xai). IEEE Access 6: 52138–52160.
• Akcora, C. G., Y. Li, Y. R. Gel, and M. Kantarcioglu, 2021 Bitcoinheist: Topological data analysis for ransomware detection on the bitcoin blockchain. IEEE Transactions on Information Forensics and Security 16: 1966–1980.
• Al-Yahyaee, K. H.,W. Mensi, H. U. Ko, S. M. Yoon, and S. H. Kang, 2018 Efficiency, multifractality, and the long-memory property of the bitcoin market. Physica A 502: 127–134.
• Bartoletti, M., B. Pes, and S. Serusi, 2018 Data mining for detecting bitcoin ponzi schemes. In 2018 Crypto Valley Conference on Blockchain Technology, pp. 75–84.
• Breiman, L., 2001 Random forests. Machine Learning 45: 5–32.
• Chainalysis, 2024 The 2024 crypto crime report.
• Chen, Z., E. N. Teoh, A. Nazir, E. K. Karuppiah, and K. S. Lam, 2021 Machine learning techniques for anti-money laundering (aml) solutions in suspicious transaction detection: A review. Knowledge and Information Systems 63: 245–285.
• Cohen, J., 1988 Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum Associates, second edition.
• Fanusie, Y. and T. Robinson, 2018 Bitcoin laundering: An analysis of illicit flows into digital currency services.
• Fawcett, T., 2006 An introduction to roc analysis. Pattern Recognition Letters 27: 861–874.
• Foley, S., J. R. Karlsen, and T. J. Putnins, 2019 Sex, drugs, and bitcoin: How much illegal activity is financed through cryptocurrencies? The Review of Financial Studies 32: 1798–1853.
• Lahmiri, S., S. Bekiros, and A. Salvi, 2018 Long-range memory, distributional variation and randomness of bitcoin volatility. Chaos, Solitons & Fractals 107: 43–48.
• Lorenz, J., M. I. Silva, D. Aparicio, J. T. Ascensao, and P. Bizarro, 2020 Machine learning methods to detect money laundering in the bitcoin blockchain in the presence of label scarcity. In Proceedings of the First ACM International Conference on AI in Finance.
• Mann, H. B. and D. R. Whitney, 1947 On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics 18: 50–60.
• Marwan, N., M. C. Romano, M. Thiel, and J. Kurths, 2007 Recurrence plots for the analysis of complex systems. Physics Reports 438: 237–329.
• Monamo, P., V. Marivate, and B. Twala, 2016 Unsupervised learning for robust bitcoin fraud detection. In Information Security for South Africa.
• Paquet-Clouston, M., B. Haslhofer, and B. Dupont, 2019 Ransomware payments in the bitcoin ecosystem. Journal of Cybersecurity 5.
• Pedregosa, F. e. a., 2011 Scikit-learn: Machine learning in python. Journal of Machine Learning Research 12: 2825–2853.
• Pham, T. and S. Lee, 2016 Anomaly detection in bitcoin network using unsupervised learning methods. arXiv preprint arXiv:1611.03941 .
• Rawald, T., M. Sips, N. Marwan, and D. Dransch, 2017 Fast computation of recurrences in long time series. In Discovery Science.
• Rossi, E., B. Chamberlain, F. Frasca, D. Eynard, F. Monti, et al., 2020 Temporal graph networks for deep learning on dynamic graphs. arXiv preprint arXiv:2006.10637 .
• Strozzi, F., J. M. Zaldivar, and J. P. Zbilut, 2002 Application of nonlinear time series analysis techniques to high-frequency currency exchange data. Physica A 312: 520–538.
• Takaishi, T., 2018 Statistical properties and multifractality of bitcoin. Physica A 506: 507–519.
• Takens, F., 1981 Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980.
• Wallot, S. and D. Monasterio, 2018 Calculation of average mutual information (ami) and false-nearest neighbors (fnn). Frontiers in Psychology 9: 1679.
• Webber, C. L. and J. P. Zbilut, 2005 Recurrence quantification analysis of nonlinear dynamical systems. In Tutorials in Contemporary Nonlinear Methods for the Behavioral Sciences, edited by M. A. Riley and G. C. Van Orden, pp. 26–94, National Science Foundation.
• Weber, M. e. a., 2019 Anti-money laundering in bitcoin: Experimenting with graph convolutional networks for financial forensics. In KDD ’19 Workshop on Anomaly Detection in Finance.
• Xu, D., C. Ruan, E. Korpeoglu, S. Kumar, and K. Achan, 2020 Inductive representation learning on temporal graphs. In International Conference on Learning Representations (ICLR).
• Zunino, L., M. Zanin, B. M. Tabak, D. G. Perez, and O. A. Rosso, 2010 Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency. Physica A 389: 1891–1901.