Shock waves and adiabatic trapping in relativistic quantum degenerate plasmas: Exploring periodic, quasiperiodic and chaotic behavior

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Zeeshan Iqbal , H.A. Shah , M.N.S. Qureshi , Eihab M. Abdel-Rahman
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Abstract

Ion acoustic shock waves are investigated in relativistic quantum degenerate plasmas, which are characterized by their ultra-high densities. Our investigation employs a nonlinear equation that has a 3/2 order fractional power. We investigate the intricate interplay between the adiabatically trapped electrons and the shock front by employing phase portrait analysis of a planar dynamical system that has not been considered earlier. This exploration allows us to understand the effects of various controlling parameters on the shock profile, steepness, and associated dynamics. An external periodic force is introduced in the current mathematical model to investigate the quasiperiodic and chaotic behavior of the system. Additionally, Poincaré sections, Fast Fourier Transformations, bifurcation analysis, and sensitivity analysis are performed to reveal the quasiperiodic and chaotic nature of the attractor of the nonlinear dynamical system. It is observed that the commensurable and incommensurable characteristics of the natural frequency and external periodic force frequency of the system play a significant role in the system's quasiperiodic and chaotic behavior. The findings not only deepen our understanding of shock waves in relativistic quantum degenerate plasmas but also have broader implications for various applications in astrophysics and nonlinear dynamics. This work also highlights the quasiperiodic and chaotic behavior of the system as the external periodic force varies by considering the commensurability of the system's frequencies.
相对论量子退化等离子体中的冲击波和绝热捕获:探索周期、准周期和混沌行为
我们研究了相对论量子退化等离子体中的离子声冲击波,这种等离子体的特点是密度超高。我们的研究采用了一个具有 3/2 阶分数幂的非线性方程。通过对平面动力学系统进行相位肖像分析,我们研究了绝热被困电子和冲击前沿之间错综复杂的相互作用,而这在之前的研究中还没有考虑过。这种探索使我们能够理解各种控制参数对冲击轮廓、陡度和相关动力学的影响。当前的数学模型引入了外部周期力,以研究系统的准周期和混沌行为。此外,还进行了波恩卡列截面、快速傅立叶变换、分岔分析和敏感性分析,以揭示非线性动力系统吸引子的准周期和混沌性质。研究发现,系统的固有频率和外部周期力频率的可通约性和不可通约性特征在系统的准周期和混沌行为中起着重要作用。这些发现不仅加深了我们对相对论量子退化等离子体中冲击波的理解,而且对天体物理学和非线性动力学的各种应用具有更广泛的意义。这项工作还通过考虑系统频率的可比性,强调了系统在外部周期力变化时的准周期和混沌行为。
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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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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