A Nonlinear Megastable System with Diamond-Shaped Oscillators

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2024-03-19 DOI:10.1142/s0218127424500536

Atefeh Ahmadi, Sridevi Sriram, Ahmed M. Ali Ali, Karthikeyan Rajagopal, Nikhil Pal, Sajad Jafari

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引用次数: 0

Abstract

Benefiting from trigonometric and hyperbolic functions, a nonlinear megastable chaotic system is reported in this paper. Its nonlinear equations without linear terms make the system dynamics much more complex. Its coexisting attractors’ shape is diamond-like; thus, this system is said to have diamond-shaped oscillators. State space and time series plots show the existence of coexisting chaotic attractors. The autonomous version of this system was studied previously. Inspired by the former work and applying a forcing term to this system, its dynamics are studied. All forcing term parameters’ impacts are investigated alongside the initial condition-dependent behaviors to confirm the system’s megastability. The dynamical analysis utilizes one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents, Kaplan–Yorke dimension, and attraction basin. Because of this system’s megastability, the one-dimensional bifurcation diagrams and Kaplan–Yorke dimension are plotted with three distinct initial conditions. Its analog circuit is simulated in the OrCAD environment to confirm the numerical simulations’ correctness.

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带菱形振荡器的非线性巨稳系统

受益于三角函数和双曲函数，本文报告了一个非线性巨稳混沌系统。它的非线性方程没有线性项，使得系统动力学变得更加复杂。其共存吸引子的形状类似钻石，因此，该系统被称为钻石型振荡器。状态空间和时间序列图显示了共存混沌吸引子的存在。以前曾研究过该系统的自主版本。在前人研究的启发下，我们对该系统施加了强迫项，研究了它的动力学特性。在研究初始条件相关行为的同时，还研究了所有强制项参数的影响，以确认系统的巨稳性。动力学分析利用了一维和二维分岔图、Lyapunov 指数、Kaplan-Yorke 维度和吸引盆地。由于该系统的巨稳性，一维分岔图和 Kaplan-Yorke 维度是在三个不同的初始条件下绘制的。为了证实数值模拟的正确性，还在 OrCAD 环境中模拟了其模拟电路。

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

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.