| 一个分数阶小世界网络模型的稳定性与Hopf分岔延迟控制 |
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| 引用本文： | 石敏,王在华.一个分数阶小世界网络模型的稳定性与Hopf分岔延迟控制[J].中国科学(G辑),2013(4):467-477. |
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| 作者姓名： | 石敏 王在华 |
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| 作者单位： | [1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016 [2]解放军理工大学理学院应用数理系,南京211101 |
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| 基金项目： | 国家杰出青年科学基金资助项目（编号：10825207） |
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| 摘 要： | 本文首先将一个含时滞的小世界网络模型推广到分数阶情形，然后详细讨论了其唯一正平衡点的稳定性切换与Hopf分岔，得到了稳定性区间的显式表达式和发生Hopf分岔的条件，进而采用Pyragas型时滞反馈控制，使得即使在较强非线性因素条件下，通过适当增大增益取值和调节分数阶的阶次，可显著延迟受控系统的Hopf分岔发生，从而大大提高网络系统平衡点的稳定性．数值算例验证了理论的正确性．
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| 关 键 词： | 分数阶 时滞 小世界网络 稳定性 Hopf分岔 分岔控制 |
Stability and Hopf bifurcation control of a fractional-order small world network model |
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| Authors: | SHI Min ＆ WANG ZaiHua |
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| Affiliation: | SHI Min ＆ WANG ZaiHua (1 State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2 Institute of Science, PLA University of Science and Technology, Nanjing 211101, China) |
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| Abstract: | In this paper, a fractional-order model is firstly proposed for a small world network with time-delay, where the fractionalorder derivative is used to reflect the self-similarity of the network. Then by using the method of stability switches, the stability and Hopf bifurcation of the generalized small world network with time-delay are studied. Explicit conditions for describing the stability interval and emergence of Hopf bifurcation are obtained. Further, the Pyragas type delayed feedback control is used to delay the onset of Hopf bifurcation by increasing the gain and changing the fractional-order. Numerical examples show that the stability of the controlled system can be improved substantially. |
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| Keywords: | fractional-order derivative time-delay small world stability Hopf bifurcation bifurcation control |
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