Synchronization and coherence resonance in chaotic neural networks

Synchronization and coherence of chaotic Morris-Lecar （ML） neural networks have been investigated by numerical methods. The synchronization of the neurons can be enhanced by increasing the number of the shortcuts, even though all neurons are chaotic when uncoupled. Moreover, the coherence of the neurons exhibits a non-monotonic dependence on the density of shortcuts. There is an optimal number of shortcuts at which the neurons＇ motion is most ordered, i.e. the order parameter （the characteristic correlation time） that is introduced to measure the coherence of the neurons has a maximum. These phenomena imply that stochastic shortcuts can tame spatiotemporal chaos. The effects of the coupling strength have also been studied. The value of the optimal number of shortcuts goes down as the coupling strength increases.  

一种基于混沌系统部分序列参数辨识的混沌保密通信方法

本文提出一种混沌保密通信方法，即混沌系统的部分序列用于混沌系统参数辨识其他序列用于通信保密. 利用混沌蚁群优化算法对部分序列混沌系统进行参数辨识，以达到了解混沌系统全部信息的目的. 在参数辨识过程中引入参数空间和蚁群空间，通过空间变换函数使参数空间与蚁群空间之间相互变换. 文中使用Lorenz系统进行数值试验，其结果验证混沌系统部分序列参数辨识及混沌保密通信的可行性. 关键词： 混沌蚁群优化 参数辨识 混沌保密通信 数值模拟  

System-Size induced Coherence Resonance in Coupled Minimal Cytosolic Ca^2＋ Oscillation Models

We have investigated the collective behaviour of an array of coupled minimal cytosotic Ca^2＋ oscillation models by numerical methods, taking into account the external noise resulting from the random extracellular stimulation. It is found that the system size, i.e. the number of minimal cytosolic Ca^2＋ oscillation models, has an optimal value, at which the system collective dynamics shows the best performance. The effect of the coupling strength has also been studied. Such a phenomenon of system-size resonance has been found for different coupling strengths, but the optimal system size increases when the coupling strength increases.  

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.  

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.  

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.  

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.  

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.  

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.