二流体磁化等离子体振荡器在参数激励下的轨道和混沌

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED
Sengen Hu, Liangqiang Zhou
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引用次数: 0

摘要

摘要本文研究了两流体磁化等离子体振荡器在参数激励下的平方延迟反馈。详细讨论了三井和窄单井的Hamilton系统。给出了相画像和平衡的情形。严格推导了同斜轨道和异斜轨道。利用Melnikov方法,解析导出了同斜或异斜交点混沌的临界值。我们发现了一些有趣的动力学现象,如不可控的时间延迟,混沌总是在这个系统中发生。研究了时滞对混沌特性的影响。在理论分析的基础上,给出了时间历程、相图、分岔图、庞加莱剖面、李雅普诺夫指数谱和吸引子盆地等数值模拟结果。数值模拟结果与理论结果一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback
Abstract In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.
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来源期刊
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
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