Construction and Analysis of a New Seven-Dimensional Chaotic System with Complex Dynamical Behaviors - Shnawa, Sura Hasballah; Mehdi, Sadiq A.; Abdul Kareem, Emad I. (IIUM Engineering Journal, 2025)
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.