Chaotic Pattern and Solitary Solutions for the (21)-Dimensional Beta-Fractional Double-Chain DNA System

Fractal and Fractional Pub Date : 2024-07-15 DOI:10.3390/fractalfract8070415

T. Han, Kun Zhang, Yueyong Jiang, Hadi Rezazadeh

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Abstract

The dynamical behavior of the double-chain deoxyribonucleic acid (DNA) system holds significant implications for advancing the understanding of DNA transmission laws in the realms of biology and medicine. This study delves into the investigation of chaos patterns and solitary wave solutions for the (2+1) Beta-fractional double-chain DNA system, employing the theory of planar dynamical systems and the method of complete discrimination system for polynomials (CDSP). The results demonstrate a diverse spectrum of solitary wave solutions, sensitivity to perturbations, and manifestations of chaotic behavior within the system. Through the utilization of the complete discrimination system for polynomials, a multitude of novel solitary wave solutions, encompassing periodic, solitary wave, and Jacobian elliptic function solutions, were systematically constructed. The influence of Beta derivatives on the solutions was elucidated through parameter comparison analysis, emphasizing the innovative nature of this study. These findings underscore the potential of this system in unraveling various biologically significant DNA transmission mechanisms.

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21 维贝塔分数双链 DNA 系统的混沌模式和孤解

双链脱氧核糖核酸（DNA）系统的动力学行为对促进生物学和医学领域对 DNA 传递规律的理解具有重要意义。本研究运用平面动力系统理论和多项式完全判别系统（CDSP）方法，深入研究了（2+1）贝塔分数双链 DNA 系统的混沌模式和孤波解。研究结果表明，该系统中存在多种孤波解、对扰动的敏感性和混沌行为表现。通过利用完整的多项式判别系统，系统地构建了大量新颖的孤波解，包括周期解、孤波解和雅各布椭圆函数解。通过参数比较分析，阐明了 Beta 导数对解法的影响，强调了这项研究的创新性。这些发现强调了该系统在揭示各种具有生物学意义的 DNA 传输机制方面的潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fractal and Fractional

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