Neural Signal Tuned by Random Long-range Connections in Coupled FitzHugh-Nagumo Neurons Systems

We investigate the effect of random long-range connections on signal propagation in an array of coupled FitzHugh- Nagumo （FHN） neurons. The neural network can be obtained by randomly adding a small fraction of shortcuts in an originally locally coupled one-dimensional chain. It is shown that when the first neuron is subjected to external stimuli, it fires and excites its connected neighbours, such that the neural signal may propagate along the chain favoured by the shortcuts. Moreover, there exists an optimal number of shortcuts which can lead to the most synchronous behaviour. In addition, how the region of the fraction of shortcuts varies with the coupling strength is also discussed. These results suggest that topological disorder in the neural network may play a vital role in helping information processing in living systems.     

T h e r mo C a l c软件在二元体系相图中的应用研究

借助T h e r mo C a l c软件中 W i n d o w s图形操作界面和强大的相图绘制功能, 仿真模拟了二元凝聚体系 相变过程. 首先, 利用该软件模拟绘制两典型的二元合金的相图, 然后, 利用杠杆定则, 从相图中计算出平衡条件下 的相成分和相应的热力学数据. 使用该软件, 既可快速准确地计算各种热力学过程, 获得材料相关参数, 又可以节约 时间和降低设计开发的成本, 更重要的是让学生掌握用计算机仿真解决实际问题的基本方法, 充分调动他们学习的 积极性和提高他们参与教学科研的自主创新热情     

Adaptive co-evolution of strategies and network leading to optimal cooperation level in spatial prisoner’s dilemma game

We study evolutionary prisoner’s dilemma game on adaptive networks where a population of players co-evolves with their interaction networks.During the co-evolution process,interacted players with opposite strategies either rewire the link between them with probability p or update their strategies with probability 1 p depending on their payoffs.Numerical simulation shows that the final network is either split into some disconnected communities whose players share the same strategy within each community or forms a single connected network in which all nodes are in the same strategy.Interestingly,the density of cooperators in the final state can be maximised in an intermediate range of p via the competition between time scale of the network dynamics and that of the node dynamics.Finally,the mean-field analysis helps to understand the results of numerical simulation.Our results may provide some insight into understanding the emergence of cooperation in the real situation where the individuals’ behaviour and their relationship adaptively co-evolve.     

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.     

Synchronized Anti-Phase and In-Phase Oscillations of Intracellular Calcium Ions in Two Coupled Hepatocytes System

We study the dynamic behaviour of two intracellufar calcium oscillators that are coupled through gap junctions both to Ca^2＋ and inositol（1,4,5）-trisphosphate （IP3）. It is found that synchronized anti-phase and in-phase oscillations of cytoplasmic cadcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP3 synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca^2＋ and IP3 among cells on synchronous behaviour, are considered. We fnd that small coupling of Ca^2＋ and large coupling of IP3 facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling.     

Amplified Signal Response by Neuronal Diversity on Complex Networks

The effect of diversity on dynamics of coupled FitzHugh-Nagumo neurons on complex networks is numerically investigated, where each neuron is subjected to an external subthreshold signal. With the diversity the network is a mixture of excitable and oscillatory neurons, and the diversity is determined by the variance of the system＇s parameter. The complex network is constructed by randomly adding long-range connections （shortcuts） on a nearest-neighbouring coupled one-dimensional chain. Numerical results show that external signals are maximally magnified at an intermediate value of the diversity, as in the case of well-known stochastic resonance, burthermore, the effects of the number of shortcuts and coupled strength on the diversity-induced phenomena are also discussed. These findings exhibit that the diversity may play a constructive role in response to external signal, and highlight the importance of the diversity on such complex networks.     

噪声在非线性化学体系中作用的研究现状

本文综述了噪声的种类、来源、统计性质、作用机制和在不同体系中噪声诱导的丰富的非线性的动力学行为, 重点叙述了噪声在非线性化学体系中的重要作用及其应用。     

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.     

两种体系中多重随机共振的噪声调控

通过计算机模拟,介绍一种新的方法来控制两种体系中的多重随机共振,被控参数选为噪声的脉冲间隔或噪声强度。对于对称的二能级的量子耗散体系,调节量子噪声则可以实现对量子多重随机共振的控制。另外还借用不同能级之间跃迁的来解释多重随机共振现象的形成机理。     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper,by the help of evolutionary algorithm and using Hindmarsh–Rose(HR)neuron model,we investigate the efect of topology structures on synchronization transition between diferent states in coupled neuron cells system.First,we build diferent coupling structure with N cells,and found the efect of synchronized transition contact not only closely with the topology of the system,but also with whether there exist the ring structures in the system.In particular,both the size and the number of rings have greater efects on such transition behavior.Secondly,we introduce synchronization error to qualitative analyze the efect of the topology structure.Furthermore,by fitting the simulation results,we find that with the increment of the neurons number,there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems.Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system.Biological system may gradually acquire such efcient topology structures through the long-term evolution,thus the systems’information process may be optimized by this scheme.