Construction and Analysis of a New Seven-Dimensional Chaotic System with Complex Dynamical Behaviors

Sura Hasballah Shnawa; Sadiq A. Mehdi; Emad I. Abdul Kareem

doi:10.31436/iiumej.v26i3.3590

Authors

Sura Hasballah Shnawa Mustansiriyah University https://orcid.org/0009-0002-0672-4491
Sadiq A. Mehdi Mustansiriyah University https://orcid.org/0000-0003-2214-5772
Emad I. Abdul Kareem Mustansiriyah University

DOI:

https://doi.org/10.31436/iiumej.v26i3.3590

Keywords:

HyperChaotic, Seven Dimensional, Dynamic Analysis, Lyapunov exponent, Equilibrium points

Abstract

This work presents a novel seven-dimensional hyperchaotic system with six Lyapunov exponents, three of which are positive, confirming chaotic behavior. The proposed system exhibits intricate dynamic behavior. This makes it highly suitable for various applications, particularly in secure communication. The system's key properties were analyzed using Lyapunov exponents, where the highest exponent is "6.68949", further confirming its strong chaotic nature. Additionally, bifurcation diagrams, phase portraits, equilibrium points, the Kaplan-Yorke dimension, and multistability were examined, providing a comprehensive understanding of its complex dynamics. Other important characteristics, including dissipativity, waveform analysis, sensitivity to initial conditions, and keyspace analysis, were also investigated to validate the system's robustness and applicability. A Mathematica model generated phase images of several strange attractors to support the theoretical findings.

ABSTRAK: Karya ini mempersembahkan sistem hiperchaotic tujuh dimensi novel dengan enam eksponen Lyapunov, tiga daripadanya positif, mengesahkan tingkah laku huru-hara. Sistem yang dicadangkan mempamerkan tingkah laku dinamik yang rumit. Ini menjadikannya sangat sesuai untuk pelbagai aplikasi, terutamanya dalam komunikasi selamat. Sifat utama sistem dianalisis menggunakan eksponen Lyapunov, di mana eksponen tertinggi ialah "6.68949", seterusnya mengesahkan sifat huru-hara yang kuat. Selain itu, gambar rajah bifurkasi, potret fasa, titik keseimbangan, dimensi Kaplan-Yorke, dan kestabilan berbilang telah diperiksa, memberikan pemahaman menyeluruh tentang dinamik kompleksnya. Ciri penting lain, termasuk dissipativity, analisis bentuk gelombang, kepekaan kepada keadaan awal dan analisis ruang kekunci, juga disiasat untuk mengesahkan keteguhan dan kebolehgunaan sistem. Menggunakan model MATHEMATICA, imej fasa beberapa penarik pelik dijana untuk menyokong penemuan teori.

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References

Skinner JE, Molnar M, Vybiral T, Mitra M. (1992) Application of chaos theory to biology and medicine. Integrative Physiological and Behavioral Science, 27:39-53.

Ewees AA, Abd Elaziz M. (2020) Performance analysis of chaotic multi-verse harris hawks optimization: a case study on solving engineering problems. Engineering Applications of Artificial Intelligence, 88:103370. https://doi.org/10.1016/j.engappai.2019.103370

AL-Hashemy RH, Mehdi SA. (2019) A new algorithm based on magic square and a novel chaotic system for image encryption. Journal of Intelligent Systems, 29(1):1202-15. https://doi.org/10.1515/jisys-2018-0404

Lorenz EN. (1963) Deterministic nonperiodic flow. Journal of atmospheric sciences,20(2):130-41. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

Lu J, Chen G, Yu X, Leung H. (2004) Design and analysis of multiscroll chaotic attractors from saturated function series. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(12):2476-90. https://doi.org/10.1109/TCSI.2004.838151

Shakir HR, Hattab AA, Mehdi SA. (2022) A dynamic S-box generation based on a hybrid method of new chaotic system and DNA computing. TELKOMNIKA (Telecommunication Computing Electronics and Control), 20(6):1230-8. http://doi.org/10.12928/telkomnika.v20i6.23449

Rössler OE. (1976) An equation for continuous chaos. Physics Letters A, 57(5):397-8. https://doi.org/10.1016/0375-9601(76)90101-8

Jia Q. (2007) Hyperchaos generated from the Lorenz chaotic system and its control. Physics Letters A, 366(3):217-22. https://doi.org/10.1016/j.physleta.2007.02.024

Lagmiri SN, Amghar M, Sbiti N. (2017) Hyperchaos based cryptography: New seven- dimensional systems to secure Communications. Circ. Comput Sci, 2(2):20-30.

Sadkhan SB, Mehdi SA, Zghair HK. (2020) Analysis of Novel Seven-Dimension Hyper Chaotic by Using SDIC and Waveform. In proceedings of the 3rd International Conference on Engineering Technology and its Applications (IICETA): 2020; IEEE, pp. 95-99. https://doi.org/10.1109/IICETA50496.2020.9318940

Sun S, Guo Y, Wu R. (2019) A novel image encryption scheme based on 7D hyperchaotic system and row-column simultaneous swapping. IEEE Access, 7:28539-47. https://doi.org/10.1109/ACCESS.2019.2901870

Kopp M. (2024) Dynamical analysis, circuit design, synchronization, and Arduino UNO implementation of a new 7D hyperchaotic system. International Journal of Chaos Theory, 10(3): 123-134.

Singh JP, Rajagopal K, Roy BK. (2018) A new 5D hyperchaotic system with stable equilibrium point, transient chaotic behaviour and its fractional-order form. Pramana, 91:1-0.

Mehdi SA, Zghair HK, Sadkhan SB. (2021) Bifurcation of novel seven-dimension hyper chaotic system. Journal of Physics: Conference Series, 1804: 012051. IOP Publishing.

Yu W, Wang J, Wang J, Zhu H, Li M, Li Y, Jiang D. (2019) Design of a new seven-dimensional hyperchaotic circuit and its application in secure communication. IEEE Access, 7:125586-608. https://doi.org/10.1109/ACCESS.2019.2935751

Thivagar ML, Hamad AA, Tamilarasan B, Antony GK. (2022) A novel seven-dimensional hyperchaotic. InProceedings of Second Doctoral Symposium on Computational Intelligence: DoSCI 2021 2022, pp. 329-340. Springer Singapore.

Zghair HK, Mehdi SA, Sadkhan SB. (2020) Design and analytic of a novel seven-dimension hyper chaotic systems. In2020 1st Information Technology to Enhance e-learning and Other Application (IT-ELA 2020), pp. 77-81. IEEE. https://doi.org/10.1109/IT-ELA50150.2020.9253077

Vaidyanathan S, He S, Simbas A. (2021) A new multistable double-scroll 4-D hyperchaotic system with no equilibrium point, its bifurcation analysis, synchronization and circuit design. Archives of Control Sciences, 31. http://dx.doi.org/10.24425/acs.2021.136882

Wu S, Li G, Xu W, Xu X, Zhong H. (2023) Modelling and dynamic analysis of a novel seven-dimensional Hamilton conservative hyperchaotic systems with wide range of parameter. Physica Scripta, 98(5):055218.

Mehdi SA, Mohammed SJ. (2020) Web application authentication using ZKP and novel 6D chaotic system. Indonesian Journal of Electrical Engineering and Computer Science, 20(3):1522-9.