Design and Stability Analysis of Adaptive Synchronization Control Strategies for Integer and Fractional Chaotic Systems
Main Article Content
Abstract
Chaotic synchronization plays an important role in nonlinear dynamics, secure communications, and complex information systems, yet parameter uncertainty remains a major obstacle to practical implementation. This study proposes a unified adaptive synchronization control strategy for both integer-order and fractional-order chaotic systems under unknown parameter conditions. Based on Lyapunov stability theory, generalized controller structures and adaptive parameter update laws are designed to achieve robust synchronization independent of specific system forms. Stability analysis theoretically proves asymptotic synchronization and bounded convergence of parameter estimation errors. Numerical simulations using representative Lorenz and fractional-order Chen systems verify the effectiveness and robustness of the proposed method. Results demonstrate rapid synchronization error convergence and accurate parameter estimation under uncertain conditions. The proposed framework provides theoretical support for nonlinear control systems and offers application potential in secure communications, electromagnetic signal transmission, and complex dynamic network synchronization.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
M. Mohadeszadeh and N. Pariz, “An application of adaptive synchronization of uncertain chaotic system in secure communication systems,” International journal of modelling and simulation, vol. 42, no. 1, pp. 143-152, 2022, doi: 10.1080/02286203.2020.1848281.
J. Zhang, P. Wang, N. Cheng, et al., “The dynamic analysis, FPGA implementation, and adaptive synchronization control application of a multi-vortex chaotic system based on nonlinear functions,” The Journal of Supercomputing, vol. 80, no. 16, pp. 24379-24412, 2024, doi: 10.1007/s11227-024-06257-9.
H. Huang, “Investigation of a high-performance control algorithm for a unified chaotic system synchronization control based on parameter adaptive method,” Intelligent Decision Technologies, vol. 18, no. 4, pp. 3025-3039, 2024, doi: 10.3233/IDT-240178.
P. Dousseh Y, V. Monwanou A, A. Koukpémédji A, et al., “Dynamics analysis, adaptive control, synchronization and antisynchronization of a novel modified chaotic financial system: YP Dousseh et al,” International Journal of Dynamics and Control, vol. 11, no. 2, pp. 862-876, 2023, doi: 10.1007/s40435-022-01003-6.
J. Kobiolka, J. Habermann, and E. Yamakou M, “Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: a dynamical system versus machine learning approach,” Nonlinear Dynamics, vol. 113, no. 10, pp. 10989-11008, 2025, doi: 10.1007/s11071-024-10821-6.
R. Ramar and G. Mohanavel, “Dynamic analysis of new chaotic system with five scroll and two scroll attractors: offset boosting and total amplitude control, adaptive synchronization,” Journal of Applied Nonlinear Dynamics, vol. 13, no. 04, pp. 631-642, 2024, doi: 10.5890/JAND.2024.12.002.
R. Amira and F. Hannachi, “Dynamic analysis and adaptive synchronization of a new chaotic system,” Journal of Applied Nonlinear Dynamics, vol. 12, no. 04, pp. 799-813, 2023, doi: 10.5890/JAND.2023.12.012.
L. Huang, W. Li, J. Xiang, et al., “Adaptive finite-time synchronization of fractional-order memristor chaotic system based on sliding-mode control,” The European Physical Journal Special Topics, vol. 231, no. 16, pp. 3109-3118, 2022, doi: 10.1140/epjs/s11734-022-00564-z.
Q. Lai, Y. Liu, and L. Fortuna, “Dynamical analysis and fixed-time synchronization for secure communication of hidden multiscroll memristive chaotic system,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 71, no. 10, pp. 4665-4675, 2024, doi: 10.1109/TCSI.2024.3434551.
P. Singh P, M. Borah, A. Datta, et al., “Integer cum fractional ordered active-adaptive synchronization to control vasospasm in chaotic blood vessels to reduce risk of COVID-19 infections,” International Journal of Computer Mathematics, vol. 102, no. 1, pp. 14-28, 2025, doi: 10.1080/00207160.2022.2163167.
P. Pal, V. Mukherjee, and G. Jin G, “Adaptive chaos synchronization of a mechanical system with disturbances and uncertainties,” Mathematics and Mechanics of Complex Systems, vol. 10, no. 3, pp. 245-263, 2022, doi: 10.2140/memocs.2022.10.245.
A. Boulkroune, A. Boubellouta, A. Bouzeriba, et al., “Practical finite-time fuzzy synchronization of chaotic systems with non-integer orders: two chattering-free approaches,” Journal of Systems Science and Systems Engineering, vol. 34, no. 3, pp. 334-359, 2025, doi: 10.1007/s11518-024-5635-7.
L. Chen, M. Xue, M. Lopes A, et al., “New synchronization criterion of incommensurate fractional-order chaotic systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 71, no. 1, pp. 455-459, 2023, doi: 10.1109/TCSII.2023.3297174.
S. Emiroglu, A. Akgül, Y. Adıyaman, et al., “A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization,” Circuit World, vol. 48, no. 2, pp. 265-277, 2022, doi: 10.1108/CW-09-2020-0223.
D. Khattar, N. Agrawal, and G. Singh, “Chaos synchronization of a new chaotic system having exponential term via adaptive and sliding mode control,” Differential Equations and Dynamical Systems, vol. 33, no. 2, pp. 475-493, 2025, doi: 10.1007/s12591-023-00635-0.