Article
| Title: | Improving secure communication and image encryption through fixed-time AGHPS under external disturbances (English) |
| Author: | Ouahabi, Rabiaa |
| Author: | Soula, Yamina |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 71 |
| Issue: | 5 |
| Year: | 2026 |
| Pages: | 779-802 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This article suggests a secure communication scheme with a new synchronization technique combining Adaptive Generalized Hybrid Projective Synchronization (AGHPS) and fixed-time stability for chaotic systems. The scheme is based on the structural flexibility of AGHPS but offers guaranteed and fast convergence under fixed-time control regardless of initial conditions. A comparative analysis with a recently published method is performed. The comparison shows a significant improvement in the synchronization time, indicating faster convergence under the same circumstances. In addition, higher performance is achieved by the new method in secure communication applications, especially encrypted image transmission and recovery. Simulations show unambiguous improvement in image recovery quality even under channel interference and parameter uncertainties, i.e., the scheme's efficiency and reliability. This contribution therefore provides a computationally effective and secure synchronization framework with significant advantages over existing approaches and therefore a fine choice for real-time chaos-based communication systems. (English) |
| Keyword: | secure communication |
| Keyword: | image encryption |
| Keyword: | Lyapunov stability |
| Keyword: | chaotic system |
| MSC: | 37C75 |
| MSC: | 93C10 |
| MSC: | 93D21 |
| MSC: | 94A60 |
| DOI: | 10.21136/AM.2026.0290-25 |
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| Date available: | 2026-10-12T13:01:19Z |
| Last updated: | 2026-10-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153802 |
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| Reference: | [1] Abarbanel, H. D. I., Rulkov, N. F., Sushchik, M. M.: Generalized synchronization of chaos: The auxiliary system approach.Phys. Rev. E 53 (1996), 4528-4535. 10.1103/PhysRevE.53.4528 |
| Reference: | [2] Cuomo, K. M., Oppenheim, A. V.: Circuit implementation of synchronized chaos with applications to communication.Phys. Rev. Lett. 71 (1993), 65-68. 10.1103/PhysRevLett.71.65 |
| Reference: | [3] Elhadj, Z.: Analysis of a new three-dimensional quadratic chaotic system.Radioeng. 17 (2008), 9-13. |
| Reference: | [4] Fu, J., Luo, R., Huang, M., Su, H.: Fixed time synchronization of a class of chaotic systems based via the saturation control.Rev. Mexicana Fís. 67 (2021), Article ID 041201, 8 pages. MR 4588819, 10.31349/RevMexFis.67.041201 |
| Reference: | [5] Ghosh, A.: Measure synchronization in interacting Hamiltonian systems: A brief review.Chaos Solitons Fractals 177 (2023), Article ID 114237, 13 pages. MR 4663390, 10.1016/j.chaos.2023.114237 |
| Reference: | [6] Hadji, M. M., Ladaci, S.: A novel secure communication scheme design using a fractional-order adaptive observer-based synchronization.J. Control Automat. Electr. Syst. 36 (2025), 267-282. 10.1007/s40313-025-01147-8 |
| Reference: | [7] Hampton, A., Zanette, D. H.: Measure synchronization in coupled Hamiltonian systems.Phys. Rev. Lett. 83 (1999), 2179-2182. 10.1103/PhysRevLett.83.2179 |
| Reference: | [8] Hamri, N., Ouahabi, R.: Modified projective synchronization of different chaotic systems using adaptive control.Comput. Appl. Math. 36 (2017), 1315-1332. Zbl 1372.37139, MR 3689004, 10.1007/s40314-015-0294-4 |
| Reference: | [9] Jaiswal, A. K., Sharma, B. B.: Cluster synchronization of networks of chaotic systems: A comprehensive review of theory and applications.IETE Technical Rev. 41 (2024), 537-556. 10.1080/02564602.2024.2341076 |
| Reference: | [10] Jia, T., Chen, X., Zhao, F., Cao, J., Qiu, J.: Adaptive fixed-time synchronization of stochastic memristor-based neural networks with discontinuous activations and mixed delays.J. Franklin Inst. 360 (2023), 3364-3388. Zbl 1508.93257, MR 4552361, 10.1016/j.jfranklin.2022.11.006 |
| Reference: | [11] Khanra, P., Ghosh, S., Alfaro-Bittner, K., Kundu, P., Boccaletti, S., Hens, C., Pal, P.: Identifying symmetries and predicting cluster synchronization in complex networks.Chaos Solitons Fractals 155 (2022), Article ID 111703. 10.1016/j.chaos.2021.111703 |
| Reference: | [12] Kingston, S. L., Kumaran, G., Ghosh, A., Kumarasamy, S., Kapitaniak, T.: Impact of time varying interaction: Formation and annihilation of extreme events in dynamical systems.Chaos 33 (2023), Article ID 123134, 12 pages. MR 4681132, 10.1063/5.0174366 |
| Reference: | [13] Kuz'menko, A. A.: Forced sliding mode control for chaotic systems synchronization.Nonlinear Dyn. 109 (2022), 1763-1775. Zbl 1520.93072, 10.1007/s11071-022-07552-x |
| Reference: | [14] Li, J., Zheng, J.: Finite-time synchronization of different dimensional chaotic systems with uncertain parameters and external disturbances.Sci. Reports 12 (2022), Article ID 15407, 11 pages. 10.1038/s41598-022-19659-7 |
| Reference: | [15] Li, Q., Yue, C.: Predefined-time modified function projective synchronization for multiscroll chaotic systems via sliding mode control technology.Complexity 2020 (2020), Article ID 6590502, 11 pages. Zbl 1445.93006, 10.1155/2020/6590502 |
| Reference: | [16] Li, X., Wen, C., Zou, Y.: Adaptive backstepping control for fractional-order nonlinear systems with external disturbance and uncertain parameters using smooth control.IEEE Trans. Syst. Man Cybernetics, Syst. 51 (2020), 7860-7869. 10.1109/TSMC.2020.2987335 |
| Reference: | [17] Liu, J., Liu, S., Sprott, J. C.: Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters.Nonlinear Dyn. 83 (2016), 1109-1121. Zbl 1349.93221, MR 3435930, 10.1007/s11071-015-2391-8 |
| Reference: | [18] Liu, M., Liu, J., Liang, J., Sun, Y., Shu, Y.: Observer-based secure synchronization control of directed complex-valued dynamical networks under link attacks.Nonlinear Dyn. 112 (2024), 12303-12318. 10.1007/s11071-024-09695-5 |
| Reference: | [19] Liu, Y., Yang, Z., Zhou, H.: Periodic self-triggered intermittent control with impulse for synchronization of hybrid delayed multi-links systems.IEEE Trans. Network Sci. Eng. 9 (2022), 4087-4100. MR 4510294, 10.1109/TNSE.2022.3195859 |
| Reference: | [20] Ma, R., Wu, J., Wu, K., Pan, X.: Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems.Nonlinear Dynam. 109 (2022), 3145-3156. 10.1007/s11071-022-07598-x |
| Reference: | [21] Morgül, "O.: Synchronization and chaotic masking scheme based on occasional coupling.Phys. Rev. E 62 (2000), 3543-3551. 10.1103/PhysRevE.62.3543 |
| Reference: | [22] Ouahabi, R., Boulezaz, C.: A novel approach to synchronizing a biological snap oscillator within a fixed time and expanding the method to various chaotic systems.J. Supercomput. 80 (2024), 18237-18259. 10.1007/s11227-024-06161-2 |
| Reference: | [23] Ouahabi, R., Hamaizia, T.: Generalized fixed-time synchronization of two different high-order hyperchaotic systems.Int. J. Dyn. Control 12 (2024), 725-736. MR 4709163, 10.1007/s40435-023-01219-0 |
| Reference: | [24] Ouahabi, R., Hamri, N.: Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters.Discrete Contin. Dyn. Syst., Ser. B 26 (2021), 2361-2370. Zbl 1477.34088, MR 4233742, 10.3934/dcdsb.2020182 |
| Reference: | [25] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems.Phys. Rev. Lett. 64 (1990), 821-824. Zbl 0938.37019, MR 1038263, 10.1103/PhysRevLett.64.821 |
| Reference: | [26] Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems.IEEE Trans. Autom. Control 57 (2012), 2106-2110. Zbl 1369.93128, MR 2957184, 10.1109/TAC.2011.2179869 |
| Reference: | [27] Priyanka, K. S. R., Soundararajan, G., Kashkynbayev, A., Nagamani, G.: Co-existence of robust output-feedback synchronization and anti-synchronization of delayed discrete-time neural networks with its application.Comput. Appl. Math. 43 (2024), Article ID 77, 28 pages. Zbl 1549.93051, MR 4700860, 10.1007/s40314-023-02575-5 |
| Reference: | [28] Rosenblum, M. G., Pikovsky, A. S., Kurths, J.: Phase synchronization of chaotic oscillators.Phys. Rev. Lett. 76 (1996), 1804-1807. 10.1103/PhysRevLett.76.1804 |
| Reference: | [29] Schröder, M., Mannattil, M., Dutta, D., Chakraborty, S., Timme, M.: Transient uncoupling induces synchronization.Phys. Rev. Lett. 115 (2015), Article ID 054101, 5 pages. 10.1103/PhysRevLett.115.054101 |
| Reference: | [30] Shi, Q., Zhao, Y., Zeng, J., Ding, Q.: Generalized time-delay reverse synchronization with error feedback coefficients.Phys. Scripta 99 (2024), Article ID 025209. 10.1088/1402-4896/ad17fd |
| Reference: | [31] Su, H., Luo, R., Fu, J., Huang, M.: Fixed time stability of a class of chaotic systems with disturbances by using sliding mode control.ISA Trans. 118 (2021), 75-82. 10.1016/j.isatra.2021.02.012 |
| Reference: | [32] Su, H., Luo, R., Fu, J., Huang, M.: Fixed time control and synchronization of a class of uncertain chaotic systems with disturbances via passive control method.Math. Comput. Simul. 198 (2022), 474-493. Zbl 1540.93054, MR 4403087, 10.1016/j.matcom.2022.03.010 |
| Reference: | [33] Vaidyanathan, S.: A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities.Far East J. Math. Sci. 84 (2014), 219-226. Zbl 1303.34010 |
| Reference: | [34] Wongvanich, N., Moonmuang, P., Roongmuanpha, N., Tangsrirat, W.: Synchronization of a seven-term chaotic 4D system using a simplified fixed-time adaptive integral nonsingular terminal sliding mode control and its circuit realization.IEEE Access 12 (2024), 106808-106821. 10.1109/ACCESS.2024.3437461 |
| Reference: | [35] Wu, Y., Wu, T., Liu, J., Xue, L.: Dynamic event-triggered fixed-time synchronization of multi-layer complex networks under denial-of-service attacks.Nonlinear Dyn. 113 (2025), 16821-16835. 10.1007/s11071-025-11034-1 |
| Reference: | [36] Zhang, W., Qi, J.: Synchronization of coupled memristive inertial delayed neural networks with impulse and intermittent control.Neural Comput. Appl. 33 (2021), 7953-7964. 10.1007/s00521-020-05540-z |
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