一类四维超混沌系统的Hopf分岔研究
Research on Hopf Bifurcation of a 4D Hyperchaotic System
DOI: 10.12677/AAM.2017.64056, PDF, HTML, XML, 下载: 1,699  浏览: 6,793  国家自然科学基金支持
作者: 陈玉明：广东技术师范学院，数学与系统科学学院，广东 广州
关键词: Lorenz型系统；超混沌；Hopf分岔；Lorenz-Type System； Hyperchaos； Hopf Bifurcation
摘要: 针对一类四维Lorenz型超混沌系统，基于中心流形及Hopf分岔相关理论，研究了该系统在原点平衡点处发生的Hopf分岔行为，得到了系统在Hopf分岔点的特性，包括分岔产生周期解的条件、周期解的分岔方向及稳定性等，并借助数值模拟验证了理论分析的正确性。
Abstract: This paper proposes a 4D Lorenz-type hyperchaotic system. Based on the center manifold theory and Hopf bifurcation theory, the Hopf bifurcation at origin of this system is investigated; complete mathematical characterizations for 4D Hopf bifurcation, including the direction of Hopf bifurcation and the stability of bifurcating period solutions are rigorously derived and studied, and numerical simulations are performed to justify the theoretical analysis.
文章引用：陈玉明. 一类四维超混沌系统的Hopf分岔研究[J]. 应用数学进展, 2017, 6(4): 474-480. https://doi.org/10.12677/AAM.2017.64056

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