二维映射神经元模型中的相干双共振

在具有稳定次阈值振荡特性的二维映射神经元模型中,研究了在没有外界输入信号时噪声对体系动力学的影响.通过数值计算发现了当体系的确定性动力学处于静息状态时,噪声可以诱导出神经元膜电位的随机振荡,而且随着噪声强度的变化,这种振荡的相干性具有两个极大值.另外我们还研究了当体系的确定性动力学处于稳定次阈值振荡及神经脉冲状态时的噪声效应,结果表明噪声对体系动力学的影响与其确定性动力学的分岔特性密切相关.     

二维映射神经元模型中频率依赖的随机共振

通过数值模拟方法, 研究了在具有稳定次阈值振荡特性的二维映射神经元体系中, 噪声对体系非线性动力学的调控作用. 通过计算发现了噪声诱导的动作电位和随机共振现象. 另外,还研究了体系的控制参数及输入信号的频率对体系动力学的影响, 发现了该体系中频率依赖的随机共振现象.关键词：二维映射神经元模型次阈值振荡高斯白噪声随机共振     

Meandering Spiral Waves Induced by Time-Periodic Coupling Strength

Effects of time-periodic coupling strength （TPCS） on spiral waves dynamics are studied by numerical computations and mathematical analyses. We find that meandering or drifting spirals waves, which are not observed for the case of constant coupling strength, can be induced by TPCS. In particular, a transition between outward petal and inward petal meandering spirals is observed when the period of TPCS is varied. These two types of meandering spirals are separated by a drifting spiral, which can be induced by TPCS when the period of TPCS is very close to that of rigidly rotating spiral. Similar results can be obtained if the coupling strength is modulated by a rectangle wave. Furthermore, a kinetic model for spiral movement suggested by Diet al., [Phys. Rev. E 85 （2012） 046216] is applied for explaining the above findings. The theoretical results are in good qualitative agreement with numerical simulations.     

Best Spatiotemporal Performance Sustained by Optimal Number of Random Shortcuts on Complex Networks

The spatial synchronization and temporal coherence of FitzHugh-Nagumo （FHN） neurons on complex networks are numerically investigated. When an optimal number of random shortcuts are added to a regular neural chain, the system can reach a state which is nearly periodic in time and almost synchronized in space. More shortcuts do not increase the spatial synchronization too much, but will obviously destroy the temporal regularity.     

Effect of Topological Connectivity on Firing Pattern Transitions in Coupled Neurons

By using the coupled model of Hindmarsh-Rose neuronal systems, we numerically investigate the effect of topology structures on the firing patterns transition （FPT）. A four-cell coupled system with all possible configurations are studied. We select the membrane current Iext as a controllable parameter, and set it to be near the left side for one of the bifurcation points. It is found that to have a response from some external stimuli with the proper amplitude and frequencies, the transition will appear between different firing states only when the cells in the system are coupled with some proper topological structures, which implies the occurrence of FPT induced by the configuration in the coupled system. Similar FPT phenomena could also be observed in a five-cell coupled system. Fbrthermore, we find that such transition behaviors may have some inherent relevance with the synchronization error and the average connective number among cells in the coupled system for different topology structures. These results suggest that the biological neuron systems may achieve an effective response to the external feeble stimulus by selecting the proper configuration and using the corresponding transition mode.     

RLC耦合回路的另一种描述

一般采用两个谐振子模型来描述RLC回路.然而两个谐振子模型是两个二阶微分方程,求解起来比较复杂.为此我们针对RLC回路体系,理论上和实验上研究了一阶微分方程的耦合模理论与两个谐振子模型之间的关联.研究表明耦合模理论可以推广到电路体系.     

生物构型对耦合Hindmarsh-Rose神经元系统响应能力的影响

利用Hindmarsh-Rose神经元模型研究了真实的生物细胞连接构型对耦合神经元系统响应能力的影响. 外界刺激信号通过细胞耦合从受刺激的神经元传递到其他神经元,合适的生物构型可以提高系统对刺激信号的响应能力和敏感度;同时,生物构型还会影响神经元系统的同步能力以及选择效应. 模拟的结果可以帮助我们理解面对不同外界刺激,生物体会协调自身结构,选择最佳的构型予以响应.     

表象变换和久期微扰理论在耦合杜芬方程中的应用

本文通过对耦合杜芬方程线性项的表象变换及非线性项的久期微扰理论的应用,将耦合杜芬方程转化为简正表象下的退耦合形式,由此可以很方便地得出耦合杜芬方程的解.为了验证该方法的正确性,设计了音叉耦合实验,观测到了振幅谱谱峰的劈裂以及"振滞回线"现象,这些实验结果都可以和之前所得的理论结果符合得很好.本文求解耦合非线性方程的方法...     

二维格子神经元网络的振动共振和非线性振动共振

本文采用数值模拟的方法, 在通过电突触耦合或化学突触耦合的二维格子神经元网络中, 研究了FitzHugh-Nagumo神经元受到双频信号输入时神经元网络对低频信号的响应特性. 结果表明:当固定受到双频输入信号的神经元在体系中所占的比例且FitzHugh-Nagumo神经元参数处于可激发区域时双频信号中的高频部分可诱导出动作电位产生, 而且随着高频输入信号强度的增加, 神经元网络对低频输入信号响应先增大后减小, 出现了极大值, 即发生了振动共振现象. 另外本文还研究了神经元网络对低频输入信号的二次谐波的响应, 同样发现了非线性振动共振现象, 并且体系对低频信号的响应随着其频率ω 的增加也产生共振现象, 即发生了双共振现象. 上述共振现象在以电突触耦合的二维格子神经元网络中和以化学突触耦合的二维格子神经元网络中都可以观察到. 当固定双频输入信号中高频输入信号强度时, 随着受到双频输入信号的神经元在体系中所占比例的变化, 电突触耦合的二维格子神经元网络对低频输入信号的响应与化学突触耦合的二维格子神经元网络对低频输入信号的响应相比有很大的不同.