时滞系统动力学近期研究进展与展望

综述了1999年以来时滞系统动力学在力学、机械工程、航空航天、生态学、生物学、神经网络、激光、电子和信息技术、保密通讯和经济学等领域的研究进展, 总结了其中的研究方法. 通过本文可以看出时滞系统普遍存在于自然和工程实际中, 即使对已经非常熟悉的简单振子,考虑到时滞的影响, 仍有许多问题有待作更深入的理论研究和新现象的发现.针对以往研究中出现的问题, 提出今后几年的发展方向、建议和展望, 同时指出了在理论上急需解决的一些科学问题,例如以时滞反馈控制为中心的控制策略、非线性因素和时滞联合作用的影响、时滞导致的多级分岔使系统呈现出复杂动力学行为、以时滞状态变量耦合为中心构成的网络系统计算模型对系统的影响等问题都是非线性动力学系统所遇到的科学基础问题. 

ADVANCES IN DYNAMICS FOR DELAYED SYSTEMS

The studies from 1999 to now on dynamics of delayed systems are reviewed in this paper. They concern mechanics, mechanical engineering, aeronautics and astronautics, ecology, biology, neural network, laser, electronics, information technology, security communication, economics and so on. The typical methods and techniques are discaussed. It is shown that the delayed systems are ubiquitous in nature and engineering. Many new problems and phenomena need to be studied and explored even for some simple and known oscillators when the effects of delays on systems are considered. Based on some existing problems in the studies, some topics for future studies are suggested, for examples, control strategies focused on delayed feedbacks, effects of combining delay with nonlinearities on systems, delay induced multiple bifurcations and complex dynamics in systems, computing models focused on net systems with delayed coupling of state variables and so on. These problems should be addressed since they do not occur in nonlinear systems without delays.