具有泄漏时滞和混合加性时变时滞复数神经网络的状态估计

研究了具有泄漏时滞、加性离散时变时滞、加性分布时变时滞复数神经网络的状态估计问题.在复数神经网络不分解条件下, 通过构造合适的Lyapunov-Krasovskii泛函, 并应用自由权矩阵、矩阵不等式和倒数凸组合法等方法, 通过可观测的输出测量来估计神经元状态, 给出了判断误差状态模型全局渐近稳定的与时滞相关的复数线性矩阵不等式.最后, 通过一个数值仿真算例验证了理论分析的有效性.     

基于事件触发控制带有多时变时滞的主从系统同步

研究了基于事件触发机制下带有多个时变时滞的主从系统同步问题.事件触发机制的提出,使得在实现主从系统同步的过程中,可以有效降低数据传输量,减轻网络带宽的压力.通过Lyapunov稳定理论和线性矩阵不等式的方法,得到了带有多时变时滞的主从系统同步的充分条件.最后,通过MATLAB仿真,验证了所提出同步准则的有效性.     

状态依赖时滞非局部扩散方程的波前解

本文主要研究状态依赖时滞非局部扩散方程的波前解,当出生函数单调时,可以得到单调行波解的存在性和非存在性,然后,由先验估计和Ikehara定理,进一步得到临界波前解的渐近性;当出生函数非单调时,通过引进两个辅助拟单调方程,也可以得到相应非拟单调条件下的存在性结果.     

更一般与年龄相关随机时滞种群方程的全局稳定性

讨论更一般的与年龄相关随机时滞种群方程的全局稳定性.如果传统假设(Lipschitz条件)缺失,与年龄相关随机时滞种群方程可能有多于一个弱解.然而,大量文献研究结果是在此类方程有唯一强解前提下获得.因此,有必要对更一般的有多于一个弱解情况进行相关概念推广.对更一般的与年龄相关随机时滞种群方程,随机稳定性概念被提出,一般的Barbashin-Krasovskii定理和Lasalle定理被建立,涵盖了多于一个弱解的情况.显然,这两个定理给出随机时滞种群方程稳定性的判定标准,并且通过实例说明定理的有效性.     

一类具时滞SIR传染病模型的动力行为

分析传染病模型的稳定性,并考虑到已感染者对易感染者的作用的时滞影响.文中首先在R_01时,构造一个Lyapunov泛函,证明了无病平衡点的全局渐近稳定性.当R_01时,证明了正平衡点的局部渐近稳定性和持久性.     

具有时滞的生态-传染病模型的定性分析北大核心

针对一类疾病在食饵中传播而把食饵分为易感和染病的时滞生态-传染病模型,以时滞(即传染病在食饵种群中的潜伏期)作为分支参数,讨论了系统正平衡点在时滞τ=0时的局部渐近稳定性,在τ>0时在一列临界值处发生了Hopf分支,并且对保持正平衡点稳定时时滞的范围也给出了估计.     

一类灰色脉冲随机时滞系统的几乎必然指数鲁棒稳定性

为了研究一类灰色脉冲随机时滞系统几乎必然指数稳定性的问题,首先利用Razumikhin方法和Lyapunov函数,给出了脉冲随机泛函微分系统几乎必然指数稳定的条件,然后基于此条件和时变灰矩阵的连续矩阵覆盖的分解技术,得到了该类灰色脉冲随机时滞系统几乎必然指数稳鲁棒定性的判据,最后通过一个数值例子说明了得判据是有效的和实用的.     

一类具潜伏期和隔离的肺结核模型分析

研究了一类具潜伏和积分时滞的肺结核模型,在模型中考虑了隔离和脉冲接种,运用脉冲时滞泛函微分方程理论,得到了传染病灭绝和系统持久的充分条件.     

一类具有时滞且带有捕食者相互残杀项的捕食模型的时空斑图

研究了一类具有时滞且带有捕食者相互残杀项的食饵-捕食者模型的动力学行为.通过数学分析,发现了不同类型的不稳定性,并且详细的给出了图灵不稳定的条件.通过一系列的数值模拟,得到了参数空间中丰富的图灵结构,分别有点状斑图、条状斑图以及点状和条状共存的斑图结构.这些结果表明,受时滞影响的带有捕食相互残杀项的捕食模型具有丰富的动力学,揭示了模型在实际生活中是非常有用的.     

用于长期神经电生理记录的自伸展电极阵列

Neural electrodes have been extensively utilized for the investigation of neural functions and the understanding of neuronal circuits because of their high spatial and temporal resolution. However, long-term effective electrophysiological recordings in free-behaving animals still constitute a challenging task, which hinders longitudinal studies on complex brain-processing mechanisms at a functional level. Herein, we demonstrate the feasibility and advantages of using a self-spreadable octopus-like electrode (octrode) array for long-term recordings. The octrode array was fabricated by enwrapping a bundle of eight formvar-coated nickel-chromium microwires with a layer of polyethylene glycol in a custom-made mold. After the electrodeposition of platinum nanoparticles, the microwires at the electrode tip were gathered together and then re-enwrapped with a thin layer of gelatin to maintain their structure and mechanical strength for implantation. Shortly after implantation (within 20 min), the biocompatible gelatin encapsulation swelled and dissolved, causing the self-spreading of the recording channels of the octrode array in the brain. The electrochemical characteristics of the electrode/neural tissue interface were investigated by electrochemical impedance spectroscopy (EIS). Four weeks after implantation, the average impedance of the octrodes (1.26 MΩ at 1 kHz) was significantly lower than that of the conventional tetrodes (1.50 MΩ at 1 kHz, p < 0.05, t-test). Additionally, the octrodes exhibited a better pseudo-capacitive characteristic and a considerably faster ion transfer rate at the electrode interface than the tetrodes. Spontaneous action potentials and local field potentials (LFPs) were also recorded in vivo to investigate the electrophysiological performance of the octrodes. The peak-to-peak spike amplitudes recorded for the octrodes were remarkably larger than those recorded for the tetrodes. The signal quality remained at approximately the same level for the four-week period, while the peak-to-peak spike amplitudes recorded for the tetrodes decreased abruptly. Moreover, the voltage amplitudes recorded by the octrodes at 1–200 Hz were notably larger than those by the tetrodes, suggesting a higher sensitivity in the recording of electrophysiological events. Furthermore, we performed immunochemical analyses on the brain tissues at post-implantation to evaluate the histocompatibility of the electrodes. Tissue responses of the octrodes were alleviated considerably, evidenced by the reduced astroglial intensity and increased neuron density around the implant site as compared to the tetrodes, which may be due to the relatively small size of each decentralized recording channel after self-spreading in vivo. Generally, the fabricated octrodes exhibited a lower electrochemical impedance value at the octrode/neural tissue interface and an increased signal quality during the long-term electrophysiological recording in freely moving mice as compared to the conventional tetrodes. All of these are desirable characteristics in neural circuit dissections in vivo.