The magnetic flux variable based on the working principle of magnetic-controlled memristors is introduced to address the electromagnetic induction problem caused by electromagnetic activities inside and outside the nervous system, providing the possibility of exploring electromagnetic regulation of network spatiotemporal behavior from the perspective of neurodynamics. This paper systematically detects the feasibility and effectiveness of electromagnetic stimulation in regulating spiral wave evolution based on a constructed two-dimensional regular neuronal network. After the negative feedback effect of electromagnetic stimulation on neuronal activity is confirmed, the regulation of periodic electromagnetic stimulation on spiral wave dynamics is quantitatively discussed with the help of three network metrics, namely spiking ratio, average membrane potential and average Hamilton energy. The results show that for two different regulatory schemes, the periodic stimulation can induce the drift or disappearance of spiral waves, which can be elucidated through the bifurcations of neuronal dynamics. Particularly, local stimulation makes the stimulated region act as a barrier by inhibiting the neuronal activity, thereby inducing the wave head to drift along a specific path or the spiral pattern to transition into a fascinating double spiral wave. These novel results of constrained drift and transition of splitting into two are first detected, enriching the dynamics of spiral waves and providing clinical guidance.

This paper systematically explores the deterministic characteristics of FitzHugh-Nagumo (FHN) systems’ response to synaptic noise in statistical sense. With the help of Gauss decoupling approximation, two substitute systems of FHN systems’ response to synaptic noise are established by ignoring the cumulants higher than the second order, and the feasibilities of using the substitute systems for response analysis are demonstrated through error analysis. Then, the deterministic analyses of FHN systems with synaptic noise are carried out by means of the two substitute systems. Numerical results show that whether it is the neuronal system or the network system, the synaptic noise can effectively regulate its dynamics, and induce the mode transitions of discharge activity. Based on the class II excitability of FHN neurons, the system activity has a nonlinear dependence on the noise parameter and the other variables of interest. Particularly, the synaptic noise not only makes the neuronal system transition from low-level to high-level narrow-amplitude oscillation by competing with the input signal, but also contributes to the response or detection of this system to weak input signals. This study reveals the deterministic characteristics of FHN systems with synaptic noise, which can provide a reference for the large-scale analysis.

This paper focuses particularly on the influence of wedge duration on spiral wave formation and the regulation of electromagnetic noise. The motion stability or periodicity of a constructed regular neuronal network system is revealed by applying the master stability function method. The effect of wedge duration and electromagnetic noise on spiral wave dynamics is quantified using defined metrics, and explained by bifurcation of neuronal activity and differentiation of neuronal populations. Research results are as follows: (1) The appearing wave head rotates and evolves into a spiral pattern due to the potential difference between neurons, which is determined by wedge duration. (2) Whether it is homogeneous or heterogeneous, electromagnetic noise can effectively regulate the evolution of spiral waves. (3) Noise excitation significantly suppresses the network firing activity and alters the electric field distribution, leading to the narrowing of spiral arm and the drift of wave head. This study not only demonstrates the importance of wedge duration for spiral wave formation, but also provides guidance for stochastically regulating the spiral wave evolution.

Parkinson's disease (PD) is mainly characterized by changes of firing and pathological oscillations in the basal ganglia (BG). In order to better understand the therapeutic effect of noninvasive magnetic stimulation, which has been used in the treatment of PD, we employ the Izhikevich neuron model as the basic node to study the electrical activity and the controllability of magnetic stimulation in a cortico-basal ganglia-thalamus (CBGT) network. Results show that the firing properties of the physiological and pathological state can be reproduced. Additionally, the electrical activity of pyramidal neurons and strong synapse connection in the hyperdirect pathway cause abnormal $ \beta $-band oscillations and excessive synchrony in the subthalamic nucleus (STN). Furthermore, the pathological firing properties of STN can be efficiently suppressed by external magnetic stimulation. The statistical results give the fitted boundary curves between controllable and uncontrollable regions. This work helps to understand the dynamic response of abnormal oscillation in the PD-related nucleus and provides insights into the mechanisms behind the therapeutic effect of magnetic stimulation.

The difference of congenital inheritance and acquired development makes the autaptic distribution in different brain regions variant. To investigate the physiological regulation of autaptic structures on the nervous system, the effects of chemical autapses with random distribution on the dynamics of Newman Watts small-world neuronal networks are systematically analyzed with the help of three network metrics. The autaptic occurring probability is first introduced to characterize the random distribution of autaptic structures. Numerical results show that the random distribution of chemical autapses can markedly modulate the electrophysiological activities of neuronal networks owing to the self-feedback function of excitatory autapses, not only promoting the transmission of neural signals, but also inducing the network level stochastic resonance and the transition of network dynamics. Particularly, the autaptic random distribution can make subthreshold or chaotic neuronal networks generate the phase synchronization phenomena and eventually evolve into the synchronous periodic discharge state, which provides a strategy to achieve the complete synchronization through pattern transition. This study reveals the ability of the stochastic characteristics of autaptic structures to alter the evolution of network spatiotemporal patterns, which could contribute to the application of autaptic structures in physiological experiments or artificial neural networks. (c) 2020 Published by Elsevier Ltd.

In transport of micro- or nanosized particles through a confined structure driven by thermal fluctuations and external forcing—a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile, such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerical results is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.

本文系统地研究了外加电磁刺激对FitzHugh-Nagumo (FHN)神经元系统动力学行为的调控作用.首先,在强非线性电磁感应的作用下,FHN神经元对外加电磁刺激的响应呈现显著的非线性变化特点,不仅能够产生混沌的放电现象,而且还出现了不同放电模式之间的转迁.其次,在电磁感应的作用下,周期振荡的电磁刺激对Newman-Watts小世界的神经元网络的脉冲放电频率和同步性都能够进行有效地调控,不仅提高了神经元网络对局部弱激励信号的探测和响应能力,而且能有效地控制网络时空斑图从相位同步到完全同步的演化.本文的研究揭示了电磁刺激对单个神经元和神经元网络系统动力学行为的显著调控能力,有待为生理上应用电磁刺激辅助治疗精神疾病提供理论指导.

The autaptic structure of neurons has the function of self-feedback, which is easily disturbed due to the quantum characteristics of neurotransmitter release. This paper focuses on the effect of conductance disturbance of chemical autapse on the electrophysiological activities of FHN neuron. First, the frequency encoding of FHN neuron to periodic excitation signals exhibits a nonlinear change characteristic, and the FHN neuron without autapse has chaotic discharge behavior according to the maximum Lyapunov exponent and the sampled time series. Secondly, the chemical autaptic function can change the dynamics of FHN neuronal system, and appropriate autaptic parameters can cause the dynamic bifurcation, which corresponds to the transition between different periodic spiking modes. In particular, the self-feedback function of chemical autapse can induce a transition from a chaotic discharge state to a periodic spiking or a quasi-periodic bursting discharge state. Finally, based on the quantum characteristics of neurotransmitter release, the effect of random disturbance from autaptic conductance on the firing activities is quantitatively studied with the help of the discharge frequency and the coefficient of variation of inter-spike interval series. The numerical results show that the disturbance of autaptic conductance can change the activity of ion channels under the action of self-feedback, which not only improves the encoding efficiency of FHN neuron to external excitation signals, but also changes the regularity of neuronal firing activities and induces significant coherent or stochastic bi-resonance. The coherent or stochastic bi-resonance phenomenon is closely related to the dynamic bifurcation of FitzHugh-Nagumo(FHN) neuronal system, and its underlying mechanism is that the disturbance of autaptic conductance leads to the unstable dynamic behavior of neuronal system, and the corresponding neuronal firing activity may transit between the resting state, the single-cycle and the multicycle spike states, thereby providing the occurring possibility for coherent or stochastic bi-resonance. This study further reveals the self-regulatory effect of the autaptic structure on neuronal firing activities, and could provide theoretical guidance for physiological manipulation of autapses. In addition, according to the pronounced self-feedback function of autaptic structure, a recurrent spiking neural network with local self-feedback can be constructed to improve the performance of machine learning by applying a synaptic plasticity rule.

To explore the feasibility of physiological manipulation of autaptic structures, the effects of autaptic connections on an FHN-ML neuronal system with phase noise stimulation are studied systematically. Firstly, according to the dynamic analysis of the FHN-ML neuron model, a saddle-node bifurcation can occur on an invariant circle. Under the action of external oscillatory current with phase noise, the neuronal firing activity is sensitive to phase noise with less intensity, and an appropriate noise intensity can induce a significant stochastic resonance phenomenon. Secondly, the chemical autaptic function can effectively regulate the neuronal discharge activity. An inhibitory autapse can not only induce the transition from depolarized resting to periodic spiking, but can also induce the FHN-ML neuron suppressed by strong phase noise to generate a pronounced intermittent high-level burst-like discharge mode when the autaptic conductance is greater than 0.1. Finally, for a two-dimensional regular FHN-ML neuronal network, a small amount of autaptic structures can induce some special waveforms to restore the propagation of nerve impulses interrupted by phase noise disturbance. This indicates the significant regulation of autapses on spatial patterns of the FHN-ML neuronal network. The study can provide some theoretical guidance for building autaptic structures in local areas to modulate the dynamic behaviors of biological neuronal systems.

A fixed-space-step method and a fixed-time-step method are presented, respectively, for solving the Stefan problems with time-dependent boundary conditions. The evolution of the moving interface and the temperature distribution in the phase change domain are simulated numerically by using two methods for melting in the half-plane and outward spherical solidification. Numerical experiment results show that the numerical results obtained from the two methods are in good agreement for the different test examples, and the two methods can be applied to solve Stefan problems in engineering practice.

With the help of a magnetic flux variable, the effects of stochastic electromagnetic disturbances on autapse Hodgkin–Huxley neuronal systems are studied systematically. Firstly, owing to the autaptic function, the inter-spike interval series of an autapse neuron not only bifurcates, but also presents a quasi-periodic characteristic. Secondly, an irregular mixed-mode oscillation induced by a specific electromagnetic disturbance is analyzed using the coefficient of variation of inter-spike intervals. It is shown that the neuronal discharge activity has certain selectivity to the noise intensity, and the appropriate noise intensity can induce the significant mixed-mode oscillations. Finally, the modulation effects of electromagnetic disturbances on a ring field-coupled neuronal network with autaptic structures are explored quantitatively using the average spiking frequency and the average coefficient of variation. The electromagnetic disturbances can not only destroy the continuous and synchronous discharge state, but also induce the resting neurons to generate the intermittent discharge mode and realize the transmission of neural signals in the neuronal network. The studies can provide some theoretical guidance for applying electromagnetic disturbances to effectively control the propagation of neural signals and treat mental illness.

在插值条件确定的情况下,如何灵活修改曲线形状是产品设计中的一个重要课题.文章构造了一种仅基于函数值,且带一个可调参数的分段线性插值函数,并讨论了其相关性质.研究结果表明,插值函数在给定区间上一致收敛于被插函数f(x);同时,根据实际设计需要,通过选取适宜的参数,可使该曲线C1连续且与原数据具有相同的凸性,以及可实现对曲线形状进行局部调控的目的.

通过对一类不连续的生态系统的稳定性问题进行了分析,得出此类问题的研究方法以及使用的工具,并利用图论的知识和Lyapunov稳定性的方法,给出了此系统全局半稳定性的一个结论.

To study the defects in lutetium aluminum garnet crystal grown by Czochraski method, samples are irradiated under ultraviolet light (UV) by 4 low pressure mercury lamps (254 nm-wavelength,36 W) placed 15 cm from the samples for 24 h at room temperature. Later,the 7 mmí7 mm surface of these samples is coated with silver films and then placed inside an evacuated cylindrical chamber,the exterior of which is submerged in liquid nitrogen during the experiment. Then, dielectric spectroscopy measurement is performed on both the irradiated and the original samples with a HP4194A impedance analyzer. The results show that the dielectric loss peaks of the irradiated samples appear relaxation effects. The dependency of these relaxation peaks on frequency indicates that the dielectric relaxation behavior is a response to the orientation polarization of a permanent dipole. It therefore can be inferred, according to the relaxation mechanism of the dipole, a certain number of defects may exist in lutetium aluminum garnet crystal.

数学建模的思想和方法在纺织科学与技术的研究中应用非常广泛，有必要对纺织专业学生数学建模能力进行系统的培养。本文首先对数学建模方法在纺织学科研究中的应用进行简单概括；然后应用多元化的教学方法，开展了一系列有关纺织专业学生数学建模能力培养的研究与实践，确保了教学质量的提高和人才培养目标的实现。

构造定时间步长方法求解一类相变热传导问题，数值模拟了相变过程中移动边界的运动及介质内温度场的变化。数值实验表明定时间步长方法求解相变热传导问题是可行的，并且具有较高的精度。

矩阵特征值在科学研究与工程实践中应用非常广泛,本文对矩阵特征值在马尔可夫链、多元函数的驻点和常系数线性微分方程组三个问题中的应用进行了研究,由此说明矩阵特征值在解决实际问题中的作用.

In order to investigate the influences upon solid melting process caused by constant heat source boundary condition,the fixed space?step method and the fixed time?step method are constructed. The evolution of moving boundary and the temperature distribution in the phase change process are studied. The simulation results of two numerical methods are compared with the exact results. The numerical simulations show that the evolutions of moving boundary in the phase change process are influenced significantly by Stefan numbers and the temperature distributions in the phase change zone show linear decreasing trends. Moreover,the simulation results of two numerical methods have high precision and also there is a good agreement between the simulation results and the exact results ,which indicate that the two numerical methods constructed are feasible. Therefore,these researches can provide a reference for solving the solid melting problem.

Two finite difference schemes, the explicit and implicit schemes, were established to solve the one-di-mensional melting problem with periodic heat source, while the moving boundary model of the melting problem was transformed to a fixed boundary model by a simple stretching of the spatial coordinate.The numerical stabilities of the explicit and implicit schemes were studied.The computational complexity and efficiency of these two schemes were compared.Also the evolution of the moving boundary and the temperature distribution were simulated numerically by u-sing these two finite difference schemes for the one-dimensional melting problem with periodic heat source.Numerical experiment results showed that the results obtained from these two schemes were in good agreement, but the computa-tional efficiency of the implicit scheme was much higher than that of the explicit scheme.