Parameter-dependent synchronization transition of coupled neurons with co-existing spiking and bursting

A firing pattern transition is simulated in the Leech neuron model, firstly from bursting to co-existence of spiking and bursting and then to spiking. The attraction domain of spiking and bursting for three different parameter values are calculated. Synchronization transition processes of two coupled Leech neurons, one is bursting and the other the co-existing spiking, are simulated for the three parameters. The three synchronization processes appear similar as the coupling strength increases, beginning from non-synchronization to complete synchronization through a complex dynamical procedure, but their detailed processes are different depending on the parameter values. The transition procedure is complex and the complete synchronization is in bursting for larger parameter values, while the process is simple with complete synchronization of spiking for smaller values. The potential relationship between complete synchronization and the attraction domain is also discussed. The results are instructive to understanding the synchronization behaviors of the coupled neuronal system with co-existing attractors.     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.     

混沌吸引子在两个周期振子耦合下的相同步

在分析了系统稳定的基础上，对非线性混沌吸引子在两个独立外周期振子耦合下的相同步进 行了研究.与一个周期振子耦合的情况不同，两个周期振子对混沌吸引子的耦合具有排他性 和竞争性，相同步在两个亚稳态交替出现，各自同步时间长度由外振子参数决定.确定了周 期外振子参数与同步时间长度的关系并与数值模拟计算结果进行了比较. 关键词： 混沌吸引子 相同步     

振幅耦合动态网络中相邻结点间的相同步

研究用适当的量化指标来刻画动态网络的相同步,为此定义了新的量化指标:相邻结点的网络平均锁相值和网络平均相频差.动态网络结点选择的是多旋转中心的Lorenz混沌振子,对Lorenz系统进行柱面坐标变换,用振幅耦合方法构造动态网络.分别对星形网络和小世界网络进行了仿真计算,结果表明随着耦合强度的增大,网络中相邻结点的两个系统之间存在相同步现象,而且相同步行为与定义的量化指标之间存在较准确的对应关系.     

Phase synchronization in two coupled chaotic neurons

Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rössler oscillators only having single time-scale mechanism. Using such a multiple time-scale model, the phase function can detect synchronization dynamics that cannot be distinguished by cross-correlation. Moreover, simulation results show that the Lyapunov exponents cannot be used as a definite criterion for the occurrence of chaotic phase synchronization for such a system. Evaluation of the phase function shows its utility in analyzing nonlinear neural systems.     

Li-ion batteries: Phase transition

Progress in the research on phase transitions during Li+extraction/insertion processes in typical battery materials is summarized as examples to illustrate the significance of understanding phase transition phenomena in Li-ion batteries.Physical phenomena such as phase transitions(and resultant phase diagrams) are often observed in Li-ion battery research and already play an important role in promoting Li-ion battery technology. For example, the phase transitions during Li+insertion/extraction are highly relevant to the thermodynamics and kinetics of Li-ion batteries, and even physical characteristics such as specific energy, power density, volume variation, and safety-related properties.     

双频驱动混沌系统的相同步和广义同步

研究了双频混沌信号驱动的混沌振子的广义同步和相同步问题.发现了反偏向的相同步和正偏向的广义同步，即响应振子可以优先与驱动强度弱的混沌信号达到相同步，而广义同步则先在驱动强的信号和响应振子间建立起来.对这些行为产生的动力学机理进行了详细地分析. 关键词： 相同步 广义同步 条件熵 平均频率     

Phase synchronization in bi-directionally coupled chaotic ratchets

We show the existence of phase synchronization in bi-directionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states. A transition from a regime where the phases rotate with different velocities to a synchronous state where the phase difference is bounded was observed as the coupling was increased. In addition, the region of synchronization in which the system is permanently phase locked was identified. In this regime, the transverse Lyapunov exponent corresponding to both phases remain positive. Our calculations show that the transition to a synchronized state occurs via a crisis transition to an attractor filling the whole phase space.     

环形耦合Duffing振子间的同步突变

以环形耦合Duffing振子系统为研究对象,分析了耦合振子间的同步演化过程.发现在弱耦合条件下,如果所有振子受到同一周期策动力的驱动,那么系统在经历倍周期分岔、混沌态、大尺度周期态的相变时,各振子的运动轨迹之间将出现由同步到不同步再到同步的两次突变现象.利用其中任何一次同步突变现象可以实现系统相变的快速判别,并由此补充了利用倍周期分岔与混沌态的这一相变对微弱周期信号进行检测的方法. 关键词： Duffing振子 同步突变 相变 微弱信号检测     

Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation

The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris-Lecar （ML） model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors： one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period- 1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period- 1 firing neuron that lead to complete synchronization of period- 1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system.     

零质量射流激励下诱发液体相变及其格子Boltzmann方法模拟

使用格子Boltzmann方法对零质量射流激励下液体的相变演化过程进行了数值模拟和分析.首先,提出了此特定零质量射流进出口边界的处理格式.然后,结合Shan和Doolen提出的单组分多相模型,模拟了方腔内液体受到此零质量射流激励而诱发产生空化的过程,着重分析了三个重要射流参数ε/T,T和v out/v in对方腔内液体相变的影响.分析表明:演化过程中方腔内气相节点数量在初始阶段急剧增长,然后经振荡趋于一个稳定值.由于ε/T和v out/v in可以反映射流在出入方腔两个过程间相互转换时的急剧变化,所以能够影响方腔中的液体相变的演化;而改变参数T并不影响射流速度的变化程度,所以T对液体相变的影响较弱.对于本文给定的参数取值,ε/T较小时,方腔内液体相变生成的孤立气泡脱离壁面;较大的ε/T下产生附着于方腔壁面的气泡,并且能够加速液体的相变进程;v out/v in的增加使方腔内相应的孤立气泡所覆盖的范围略有减小.研究结果揭示了零质量射流激励诱发的液体相变过程,为进一步探索液体空化的控制途径奠定了基础.     

Phase group synchronization between any signals and its physical characteristics

The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the timefrequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.     

简并光学参量振荡器混沌相同步与反相同步

从广泛意义上研究了简并光学参量振荡器的混沌同步. 数值结果表明, 当最大条件李指数小于零时, 处于混沌态的两个简并光学参量振荡器通过单向耦合可以实现相同步或反相同步. 当两个简并光学参量振荡器同时实现正耦合或负耦合时为相同步, 当其中一个为正耦合而另一个为负耦合时实现反相同步.     

Enhance sensitivity to illumination and synchronization in light-dependent neurons

When a phototube is activated to connect a neural circuit, the output voltage becomes sensitive to external illumination because the photocurrent across the phototube can be controlled by external electromagnetic wave. The channel currents from different branch circuits have different impacts on the outputs voltage of the neural circuit. In this paper, a phototube is incorporated into different branch circuits in a simple neural circuit, and then a light-controlled neuron is obtained for further nonlinear analysis. Indeed, the phototube is considered as exciting source when it is activated by external illumination, and two kinds of light-sensitive neurons are obtained when the phototube is connected to capacitor or induction coil, respectively. Electric synapse coupling is applied to detect possible synchronization between two functional neurons, and the energy consumption along the coupling channel via resistor is estimated. The analog circuits for the two kinds of light-sensitive neurons are supplied for further confirmation by using Multisim. It is found that two light-sensitive neurons and neural circuits can be synchronized by taming the coupling intensity carefully. It provides possible clues to understand the synchronization mechanism for eyes and artificial sensors which are sensitive to illumination. Finally, a section for open problems is supplied for further investigation about its collective behaviors in the network with/without synapse coupling.     

耦合Hindmarsh-Rose神经元的放电模式和完全同步

通过数值模拟和分岔分析的方法研究了Hindmarsh-Rose（HR）神经元的放电模式。当外加直流激励变化时，单个的神经元表现为静息态、周期性峰放电、周期性簇放电以及混沌的放电模式。利用快慢动力学分析的方法研究了HR神经元的动力学行为。当每个神经元表现为静息态、周期性放电和混沌时，两个耦合的神经元在一定的耦合强度下均会达到完全同步。神经元的耦合方式模拟神经元之间缝隙连接的电耦合。理论分析了完全同步的判断准则，并给出相应的数值模拟结果。电耦合HR神经元耦合系统的峰峰间期的分岔结构在耦合的作用下仍然能保持未耦合时的分岔结构。     

Stability of incoherence in a population of coupled oscillators

We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise.     

Phase synchronization in fractional differential chaotic systems

We propose an analytical justification for phase synchronization of fractional differential equations. This justification is based upon a linear stability criterion for fractional differential equations. We then investigate the existence of phase synchronization in chaotic forced Duffing and Sprott-L fractional differential systems of equations. Our numerical results agree with those analytical justifications.     

Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.     

Phase transition in gauge theories

In this short review we present the consequences of the spontaneously broken gauge theories will lead to when describing matter at high temperature and density. It appears various phase transitions should occur leading to the restoration of symmetry at high temperature of the originally broken one. Symmetry behaviour in external magnetic fields and in the early universe has been briefly mentioned.     

Phase transition and critical behavior of spin–orbital coupled spinel ZnV_2O_4

We present the temperature-dependent susceptibility and specific heat measurement of spinel ZnV_2O_4.The structural transition with orbital ordering and the antiferromagnetic transition with spin ordering were observed at 50 K and 37 K,respectively.By analysis of the hysteresis behavior between the specific heat curves obtained in warming and cooling processes,the structural transition was confirmed to be the first-order transition,while the antiferromagnetic transition was found to be of the second-order type.At the structural transition,the latent heat and entropy change were calculated from the excess specific heat,and the derivative of pressure with respect to temperature was obtained using the Clausius-Clapayron equation.At the magnetic transition,the width of the critical fluctuation region was obtained to be about 0.5 K by comparing with Gaussian fluctuations.In the critical region,the critical behavior was analyzed by using renormalization-group theory.The critical amplitude ratio A~+/A~- = 1.46,which deviates from the 3D Heisenburg model;while the critical exponent α is-0.011,which is close to the 3D XY model.We proposed that these abnormal critical behaviors can be attributed to strong spin-orbital coupling accompanied with the antiferromagnetic transition.Moreover,in the low temperature range(2-5 K),the Fermi energy,the density of states near the Fermi surface,and the low limit of Debye temperature were estimated to be2.42 eV,2.48 eV~(-1),and 240 K,respectively.