时滞耦合系统非线性动力学的研究进展

发布时间：2019-07-19 12:05

【摘要】：随着对自然界客观规律的深入认识,工程系统设计的精细化和复杂性要求也与日剧增.在许多耦合的动态系统设计过程中要考虑由耦合过程的时滞所引发的动力学行为,该时滞来自于与传感系统、作动系统和控制系统耦合的过程.耦合时滞也广泛存在于交通、系统生物学、电子通讯、神经和信息网络等技术中.本文首先从耦合时滞出发,在以时滞为中心的耦合系统复杂动力学机制、时滞镇定耦合系统的实验基础和实现、快慢变时滞耦合系统动力学和时滞神经网络同步和去同步4个方面,对耦合时滞诱发的动力学研究进展进行综述.着重介绍了时滞耦合系统中耦合时滞诱发的高余维分岔奇异性及新的定量分析方法、中立型时滞微分方程的规范型计算、具有耦合时滞的非线性系统中耦合时滞和非线性参数的辨识方法与实验实现、快慢变时滞耦合系统的张弛振荡、耦合时滞诱发的网络系统的同步模式切换等问题的研究进展;然后在应用方面重点介绍了车床磨削加工过程中耦合时滞诱发的颤振及其机理、具有惯性项和耦合时滞的神经网络系统中耦合时滞诱发的高余维分岔和复杂动力学、时滞动力吸振器与隔振装置的设计与实验实现.最后,从耦合时滞系统的一般性理论和工程应用两个方面展望了近期值得关注的一些问题.
[Abstract]:With the deep understanding of the objective laws of nature, the refinement and complexity of engineering system design are also increasing. In the design process of many coupled dynamic systems, the dynamic behavior caused by the time delay of the coupling process should be considered, which comes from the coupling process with the sensing system, the actuating system and the control system. Coupled time delay also widely exists in traffic, system biology, electronic communication, neural and information network and other technologies. In this paper, the research progress of coupling delay-induced dynamics is reviewed from four aspects: the complex dynamic mechanism of time-delay-centered coupling system, the experimental basis and implementation of time-delay stabilization coupling system, the dynamics of fast-slow time-delay coupled system and the synchronization and desynchronization of time-delay neural network. This paper mainly introduces the high codimensional bifurcation singularity induced by coupling delay in time-delay coupled systems and a new quantitative analysis method, the canonical calculation of neutral delay differential equations, the identification method and experimental implementation of coupled time-delay and nonlinear parameters in nonlinear systems with coupled delays, the relaxation oscillations of fast-slow and time-delay coupled systems, and the synchronous mode switching of network systems induced by coupling delays. Then, in the aspect of application, the flutter induced by coupling time delay and its mechanism in lathe grinding process, the high residual dimension bifurcation and complex dynamics induced by coupling time delay in neural network system with inertia term and coupling time delay, the design and experimental realization of time delay dynamic vibration absorber and vibration isolation device are introduced in detail. Finally, some problems worthy of attention in the near future are prospected from the general theory and engineering application of coupled time-delay systems.
【作者单位】：同济大学航空航天与力学学院;
【基金】：国家自然科学基金资助项目(11572224,11502168,11032009)
【分类号】：O175

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