| 非线性时滞动力系统的研究进展 |
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| 引用本文： | 胡海岩,王在华.非线性时滞动力系统的研究进展[J].力学进展,1999,29(4):501-512. |
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| 作者姓名： | 胡海岩 王在华 |
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| 作者单位： | 南京航空航天大学振动工程研究所 |
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| 基金项目： | 国家杰出青年科学基金!59625511 |
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| 摘 要： | 具有时滞的动力系统广泛存在于各工程领域．本文从动力学角度对时滞动力系统的研究进展作一综述，内容包括时滞动力系统的特点、研究方法、动力学热点问题的研究进展等．由于时滞动力系统的演化趋势不仅依赖于系统的当前状态，还依赖于系统过去某一时刻或若干时刻的状态，其运动方程要用泛国微分方程来描述，解空间是无穷维的．即使系统中的时滞非常小，在许多情况下也不能忽略不计．对于非线性时滞常微分方程，目前的研究思路基本上与常微分方程系统理论相平行．主要研究方法可分为时域法和频域法，前者包括Ｔａｙｌｏｒ级数法，中心流形法，Ｐｏｉｎｃａｒｅ映射法等，后者包括Ｎｙｑｕｉｓｔ法等．目前对这类系统的动力学研究主要集中在稳定性、Ｈｏｐｆ分岔、混沌等方面．研究表明：时滞动力系统具有非常丰富和复杂的动力学行为，如单变量的一维非线性时滞动力系统可发生混沌现象，与用常微分方程描述的系统有本质性差别．另一方面，人们可巧妙地利用时滞来控制动力系统的行为，如时滞反馈控制是控制混饨的主要方法之一．最后，本文展望了存在的一些问题以及近期值得关注的研究．
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| 关 键 词： | 非线性振动 时滞动力系统 稳定性 混沌 |
| 修稿时间： | : 1998-04- |
RENIEW ON NONLINEAR
DYNAMIC SYSTEMS INVOLVING TIME DELAYS |
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| HuHaiyan.RENIEW ON NONLINEAR
DYNAMIC SYSTEMS INVOLVING TIME DELAYS[J].Advances in Mechanics,1999,29(4):501-512. |
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| Authors: | HuHaiyan |
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| Abstract: | From the viewpoint of dynamics, this review outlines the recent advances in the studyof nonlinear dynamic systems involving time delays, an important class of dynamic systems invarious engineering fields. The survey is made in three aspects as follows: the dynamic features,available approaches and advances in research on most attractive problems. The evolution of adelayed system depends not only on the current state of the system, but also on previous ones.Hence, a delayed dynamic system should be modeled by a functional differential equation, thesolution space of which is of infinite dimensions. IN many applications, the time delays have to betaken into account even if they are very short. At present, the studies on delayed dynamic systemsare basically parallel to those on the dynamic systems without any delay. The available approachesinclude those on time domain, such as the Taylor approximation, the center manifold reduction andtile Poincare mapping, and those on frequency domain, such as the Nyquist method. Regardingto the dynamics of delayed systems, most attention has been paid to the stability criteria of linearsystems, the Hopf bifurcation and chaotic behavior of nonlinear systems. The studies indicate thatthe delayed dynamic systems may involve very complicated dynamics. For example, a nonlineardelayed system of single state variable may exhibit chaotic behavior. This is totally different fromthe dynamic behavior of systems described by ordinary differential equations. On the other hand,an artificially introduced delay in the feedback can play am essential role in stabilizing the chaoticmotion of a nonlinear dynamic system. Finally, the review addresses a number of open problemsand suggests a few prospective research topics in a near future. |
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| Keywords: | nonlinear vibration dynamics of nonlinear systems involving time delays stability chaos and bifurcation differential equation |
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