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ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Mathematical Finance
Volume 11 - 2025 | doi: 10.3389/fams.2025.1554690
Chaos Management and Synchronization in the Liu Financial System via Sliding Mode and Passive Control
Provisionally accepted- Chittagong University of Engineering & Technology, Chittagong, Bangladesh
The Liu financial dynamical system is a chaotic model that has been extensively studied for its applicability to financial and economic activities. This work examines chaos management and synchronization in this system. Two popular control techniques in nonlinear system stabilization-Sliding Mode Control (SMC) and Passive Control (PC)-are compared. While PC makes use of the system's passivity to accomplish control goals, SMC is made to guarantee strong synchronization in the face of external disruptions and parametric uncertainties. Lyapunov theory is used for stability analysis of both approaches, guaranteeing convergence of synchronization faults. In terms of accuracy, resilience, and computational efficiency, numerical simulations show each approach's advantages and disadvantages. The findings offer important insights into how well SMC and PC work to manage unpredictability in financial systems and provide valuable guidance. Results show SMC achieves synchronization within 𝑡 ≤ 1, while PC takes 𝑡 ≤ 13. Maximum synchronization error in SMC reduces from 5.67 to 0.02, whereas PC reduces from 6.21 to 0.03. SMC, though faster, requires two controllers, whereas PC, using one controller, adjusts the interest rate for synchronization. These findings highlight the trade-offs in speed, complexity, and practical implementation of both methods for financial stability.
Keywords: Chaos, synchronization, Liu Financial Dynamical System, sliding mode control, Passive Control 1.Introduction
Received: 02 Jan 2025; Accepted: 11 Mar 2025.
Copyright: © 2025 Afroja and Akter. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Afsana Afroja, Chittagong University of Engineering & Technology, Chittagong, Bangladesh
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