SLIDING HOPF BIFURCATION IN INTERVAL SYSTEMS

Edward Hooton; Zalman Balanov; Wieslaw krawcewicz; dmitrii rachinskii

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SLIDING HOPF BIFURCATION IN INTERVAL SYSTEMS

机译：区间系统中的滑动Hopf分叉

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In this paper, the equivariant degree theory is used to analyze the occurrence of the Hopf bifurcation under effectively verifiable mild conditions. We combine the abstract result with standard interval polynomial techniques based on Kharitonov's theorem to show the existence of a branch of periodic solutions emanating from the equilibrium in the settings relevant to robust control. The results are illustrated with a number of examples.

机译：在本文中，等变度理论用于分析在可有效验证的温和条件下发生Hopf分叉的情况。我们将抽象结果与基于Kharitonov定理的标准区间多项式技术相结合，以显示存在于与鲁棒控制相关的设置中的，来自均衡的周期解的分支。结果用许多实例说明。

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《Discrete and continuous dynamical systems》 |2017年第7期|3545-3566|共22页
作者
Edward Hooton; Zalman Balanov; Wieslaw krawcewicz; dmitrii rachinskii;
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作者单位

The University of Texas at Dallas, 800 W Campbell Road Richardson, Tx 75080, USA;

The University of Texas at Dallas, 800 W Campbell Road Richardson, Tx 75080, USA;

The University of Texas at Dallas, 800 W Campbell Road Richardson, Tx 75080, USA;

The University of Texas at Dallas, 800 W Campbell Road Richardson, Tx 75080, USA;

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正文语种 eng
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关键词
Hopf bifurcation; interval polynomial; non-local branch; Kharitonov's theorem; zero exclusion principle; S~1-degree;

机译：Hopf分叉;区间多项式非本地分支;哈里托诺夫定理;零排斥原则;S〜1度;

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2. Discretizing dynamical systems with Hopf-Hopf bifurcations [J] . Chávez J.P. IMA Journal of Numerical Analysis . 2012,第1期

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3. Discretizing dynamical systems with Hopf–Hopf bifurcations [J] . Joseph Páez Chávez IMA Journal of Numerical Analysis . 2012,第1期

机译：具有Hopf–Hopf分支的离散化动力系统
4. ANALYTICAL INVESTIGATION OF HOPF BIFURCATIONS OCCURRING IN A 1DOF SLIDING-FRICTION OSCILLATOR WITH APPLICATION TO DISC-BRAKE VIBRATIONS [C] . Hartmut Hetzler, Wolfgang Seemann, Daniel Schwarzer ASME(American Society of Mechanical Engineers) International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2005(DETC2005) vol.1: 20th Biennial Conference on Mechanical Vibration and Noise pt.B . 2005

机译：一自由度滑动摩擦振动器中霍夫分叉的解析研究及其在碟刹振动中的应用
5. Hopf bifurcations in the competitive three-dimensional Lotka-Volterra systems. [D] . Zeeman, Mary Lou. 1989

机译：竞争性三维Lotka-Volterra系统中的Hopf分叉。
6. Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales [O] . Wenjun Zhang, Vivien Kirk, James Sneyd, 2011

机译：由于具有多种时标的系统中的某些模型约简技术Hopf分叉的临界度发生了变化
7. Sliding Hopf bifurcation in interval systems [O] . Hooton, E., Balanov, Z., Krawcewicz, W., 2015

机译：区间系统中的Hopf分支滑动

SLIDING HOPF BIFURCATION IN INTERVAL SYSTEMS

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