New 4-D Hyperchaotic System Derived from the Rikitake 3-D System:Properties and Application
DOI:
https://doi.org/10.56286/gyv2ss59Keywords:
Novel 4D, Hyperchaotic, Lyapunov exponents, Saddle-Focus, DissipativeAbstract
A novel 4D hyperchaotic system with two positive Lyapunov exponents is created from a Rikitake 3D system using a feedback control strategy. Several dynamical properties are investigated both theoretically and numerically, including phase, equilibrium points, divergence, root stability, and Lyapunov exponents. Additionally, using MATLAB 2021, the numerical simulation validates the veracity of the theoretical conclusions. Finally, Multisim 14.2 was used to simulate and build the electrical circuit for a new system.
Downloads
References
Al-Kateeb, Z. N., Al-Shamdeen, M. J. and Al-Mukhtar, F. S. (2020) Encryption and steganography a secret data using circle shapes in ?colored images. J. Phy.: Conf. Series, vol. 1591, pp. 012019. doi.org/10.1088/1742-6596/1591/1/012019.?
Fadhel, S. A., Al-Kateeb, Z. N. and AL-Shamdeen, M. J. (2021) An improved ?data hiding using pixel value difference method and hyperchaotic ?system. J. Phy.: Conf. Series, vol. 1879, pp. 022089. doi.org/10.1088/1742-6596/1879/2/022089. ?
Al-Khateeb, Z. N. and Jader, M. F. (2020) Encryption and hiding text using ?DNA coding and hyperchaotic system. Indones. J. Electr. Eng. ?Comput. Sci., vol.19(2), pp. 766-774. doi.org/10.11591/ijeecs.v19.i2.pp766-774.
Abed, K. A. (2020) Controlling of jerk chaotic system via linear feedback ?control strategies. Indones. J. Electr. Eng. Comput. Sci., vol. 20(1), ?pp. 370-378.? doi.org/10.11591/ijeecs.v20.i1.pp370-378.
Aziz, M. M. and Al-Azzawi, S. F. (2021) A modification of nonlinear ?feedback controller. Int. J. Comput. Sci. Math., 13(1), pp. 64-79.? doi.org/10.1504/IJCSM.2021.10038362.
Yau, H. T. and Shieh, C. S. (2008) Chaos synchronization using fuzzy logic controller. Nonlinear analysis: ?Real world ?applications, 9, 1800-1810.? doi.org/10.1016/j.nonrwa.2007.05.010.
Pai, N. S., Yau, H. T., and Kuo, C. L. (2010) Fuzzy logic combining controller design for chaos control of a ?rod-type ?plasma torch system. Expert Systems with Applications, 37, 8278-8283.? doi.org/10.1016/j.eswa.2010.05.074.
Matouk, A. (2011) Chaos, feedback control and synchronization of a fractional-order modified ?Autonomous Van der Pol–?Duffing circuit. Communications in Nonlinear Science and Numerical ?Simulation, 16, 975-986. Doi.org/10.1016/j.cnsns.2010.05.007.
Al-Talib, Z. S. and Al-Azzawi, S. F. (2023) A new simple 6D hyperchaotic system with hyperbolic equilibrium and its ?electronic circuit. 2022 8th International Conference on Contemporary Information Technology and Mathematics, ICCITM ??2022, 369–374?
Sahoo, B. and Poria, S. (2014) The chaos and control of a food chain model supplying additional food to top-??predator. Chaos, Solitons & Fractals, 58, 52-64.?? ?
Boya, B. F. B. A., Ramakrishnan, B., Effa, J. Y., Kengne, J., and Rajagopal, K. (2023) Effects of bias current and control ?of multistability in 3D hopfield neural network. Heliyon, 13034. Doi.org/10.1016/j.heliyon.2023.e13034.?
Min, F., and Luo, A. C. (2012) Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal ?constraints. Chaos, Solitons & Fractals, 45(7), 998-1011.?
Khan, A. Q., and Almatrafi, M. B. (2023) Two-dimensional discrete-time laser model with chaos and bifurcations. AIMS ?Mathematics, 8(3), 6804-6828.?
Al-Jawadi, R. Y. (2024). A comparative study on the performance of Gray Wolves Optimization and Multi-Free Dynamic Schema. NTU Journal of Pure Sciences, 3(1), 1-9.?
Al-Jawadi, R. Y. (2024). A comparative study on the performance of Gray Wolves Optimization and Multi-Free Dynamic Schema. NTU Journal of Pure Sciences, 3(1), 1-9.?
Li, S., Wu, Y., & Zhang, X. (2021) Analysis and synchronization of a new hyperchaotic system with exponential term, Mathematics, 9(24), 3281.
Nestor, T., Belazi, A., Abd-El-Atty, B., Aslam, M. N., Volos, C., De Dieu, N. J., & Abd El-Latif, A. A. (2022) A new 4D hyperchaotic system with dynamics analysis, synchronization, and application to image encryption. Symmetry, 14(2), 424.?
Zhang, S., Zeng, Y., Li, Z., Wang, M., & Xiong, L. (2018) Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(1).?
Llibre, J., & Messias, M. (2009) Global dynamics of the Rikitake system. Physica D: Nonlinear Phenomena, 238(3), 241-252.?
Singh, P. P. and Roy,B. K. (2019) Memristor-based novel complex-valued chaotic system and its projective synchronisation using nonlinear active control technique. Eur. Phys. J. Spec. Top., vol. 228(10), pp. 2197-2214.
Li, H., Shen, Y., Han, Y., Dong, J., & Li, J. (2023) Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle. Chaos, Solitons & Fractals, 168, 113167.?
Vaidyanathan, S. (2015) A novel coupled Van der Pol conservative chaotic system and its adaptive control, International Journal of PharmTech Research, 8(8), 79-94.?
Singh, J. P., and Roy, B. K. (2018) Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria. Chaos, Solitons & Fractals, 114, 81-91.?
Dong, C., and Wang, J. (2022) Hidden and coexisting attractors in a novel 4D hyperchaotic system with no equilibrium point. Fractal and Fractional, 6(6), 306.?
Prakash, P., Rajagopal, K., Koyuncu, I., Singh, J. P., Alcin, M., Roy, B. K., and Tuna, M. (2020) A novel simple 4-D hyperchaotic system with a saddle-point index-2 equilibrium point and multistability: design and FPGA-based applications. Circuits, Systems, and Signal Processing, 39(9), 4259-4280.?
Pham, V. T., Kingni, S. T., Volos, C., Jafari, S. and Kapitaniak, T. (2017) A simple three-dimensional fractional-order chaotic system without equilibrium: dynamics, circuitry implementation, chaos control and synchronization. AEU Int. J Electron Commun, vol. 78, pp. 220–227.
Tietze, U., Schenk, C., & Gamm, E. (2015). Electronic circuits: handbook for design and application. Springer.?
Gift, S. J., & Maundy, B. (2020) Electronic Circuit Design and Application. Springer Nature.?
Zhang, J., Bi, J., Hou, J., & Xie, Q. (2024). Dynamical analysis, circuit realization, and applications of 4D hyperchaotic systems with bursty oscillations and infinite attractor coexistence: J. Zhang et al. The Journal of Supercomputing, 80(7), 8767-8800.
Yan, S., Cui, Y., Li, L., Gu, B., & Ren, Y. (2023). Dynamical analysis of a novel chaotic system and its application to image encryption. Microelectronic Engineering, 279, 112054.??
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2026 Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

