时滞耦合系统非线性动力学的研究进展

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.

电机温度时滞耦合系统自抗扰控制仿真研究

电机温度过高会造成绝缘性能老化,电机安全性能下降;电机控制系统是典型的非线性系统,电机温度也因此具有时滞性和耦合性的特点,难以建立准确的数学模型;传统的方法对电机温度的控制精度较差,从而导致电机温度失控;为此,提出基于BP神经网络自抗扰控制算法的电机时滞耦合关系下温度控制方法;将BP神经网络与PID控制方法相结合建立电机温度网络自抗扰控制器模型,利用梯度下降法修正电机温度控制器模型的权值系数,从而实现了BP神经网络自抗扰控制器参数的实时调整;实验结果表明,利用BP神经网络自抗扰算法进行电机时滞耦合关系下温度调整,能够有效提高控制的精确度,缩短了控制过程中的时间延时。

一类微气泡耦合时滞系统的周期解

研究一类微气泡耦合时滞系统的稳定性以及Hopf分支,得到了稳定性和Hopf分支出现的条件,并利用泛函微分方程相关理论讨论出分支周期解的分支方向、稳定性和分支周期的变化律.

Stochastic resonance of coupled time-delayed system with fluctuation of mass and frequency and its application in bearing fault diagnosis

The stochastic resonance behavior of coupled stochastic resonance(SR)system with time-delay under mass and frequency fluctuations was studied.Firstly,the approximate system model of the time-delay system was obtained by the theory of small time-delay approximation.Then,the random average method and Shapiro-Loginov algorithm were used to calculate the output amplitude ratio of the two subsystems.The simulation analysis shows that increasing the time-delay and the input signal amplitude appropriately can improve the output response of the system.Finally,the system is applied to bearing fault diagnosis and compared with the stochastic resonance system with random mass and random frequency.The experimental results show that the coupled SR system taking into account the actual effect of time-delay and couple can more effectively extract the frequency of the fault signal,and thus realizing the diagnosis of the fault signal,which has important engineering application value.

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.

Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays

The study of synchronization and bursting transition is very important and valuable in cognitive activities and action control of brain as well as enhancement for the reliability of the cortex synapses. However, we wonder how the synaptic strength and synaptic delay, especially the asymmetrical time-delays between different neurons can collectively influence their synchronous firing behaviors. In this paper, based on the Hindmarsh-Rose neuronal systems with asymmetrical time-delays, we investigate the collective effects of various delays and coupling strengths on the synchronization and bursting transition. It is shown that the interplay between delay and coupling strength can not only enhance or destroy the synchronizations but also can induce the regular transitions of bursting firing patterns. Specifically, as the coupling strength or time-delay increasing, the firing patterns of the time-delayed coupling neuronal systems consistently present a regular transition, that is, the periods of spikes during the bursting firings increase firstly and then decrease slowly. In particular, in contrast to the case of symmetrical time-delays,asymmetrical time-delays can lead to the paroxysmal synchronizations of coupling neuronal systems, as well as the concentration level of synchronization for the non-identically coupled system is superior to the one of identical coupling. These results more comprehensively reveal the rich nonlinear dynamical behaviors of neuronal systems and may be helpful for us to have a better understanding of the neural coding.

Stability switches and bifurcation analysis in a coupled neural system with multiple delays

A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.