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.     

Non-Markovianity of the Heisenberg XY spin environment with Dzyaloshinskii–Moriya interaction

Using the effective non-Markovian measure proposed by Breuer et al. recently, we study the memory effect of a central qubit system coupled to a spin chain environment with Dzyaloshinskii-Moriya interaction in a transverse field. It is discovered that the central qubit system presents different memory effects in different environment phases with the different oscillatory behaviors of the decoherence factor. Moreover, it is revealed that the Dzyaloshinskii-Moriya interaction has a prominent influence on the memory effect of a central qubit system via modifying the amplitude and period of the decoherence factor under certain conditions.     

The isolated critical value phenomenon in local－global riddling bifurcation

A chaotic synchronized system of two coupled skew tent maps is discussed in this paper. The locally and globally riddled basins of the chaotic synchronized attractor are studied. It is found that there is a novel phenomenon in the local－global riddling bifurcation of the attractive basin of the chaotic synchronized attractor in some specific coupling intervals. The coupling parameter corresponding to the locally riddled basin has a single value which is embedded in the coupling parameter interval corresponding to the globally riddled basin, just like a breakpoint. Also, there is no relation between this phenomenon and the form of the chaotic synchronized attractor. This phenomenon is found analytically. We also try to explain it in a physical sense. It may be that the chaotic synchronized attractor is in the critical state, as it is infinitely close to the boundary of its attractive basin. We conjecture that this isolated critical value phenomenon will be common in a system with a chaotic attractor in the critical state, in spite of the system being discrete or differential.     

Superlattice Patterns in Coupled Turing Systems

In this paper, superlattice patterns have been investigated by using a two linearly coupled Brusselator model. It is found that superlattice patterns can only be induced in the sub-system with the short wavelength. Three different coupling methods have been used in order to investigate the mode interaction between the two Turing modes. It is proved in the simulations that interaction between activators in the two sub-systems leads to spontaneous formation of black eye pattern and/or white eye patterns while interaction between inhibitors leads to spontaneous formation of super-hexagonal pattern. It is also demonstrated that the same symmetries of the two modes and suitable wavelength ratio of the two modes should also be satisfied to form superlattice patterns.     

Effects of parameters on the stationary state and self-trapping of three coupled Bose-Einstein condensate solitons

The stability of three coupled Bose-Einstein condensate (BEC) solitons is investigated by the variational approach in two conventional time-independent trapping potentials. The effects of parameters of the potentials and the initial conditions of the BEC soliton system on the stationary state and self-trapping are discussed. It is found that the trapping potentials play an important role in the stability of the system and change the characteristics of the system, and there are different critical potential amplitude values corresponding to different trapping potentials and initial conditions of the BEC soliton system.     

Controlling cooperativity of a metastable open system coupled weakly to a noisy environment

The notion of cooperativity comprises a specific characteristic of a multipartite system concerning its ability to demonstrate a sigmoidal-type response of varying sensitivities to input stimuli in transitions between states under controlled conditions.From a statistical physics viewpoint,in this work we attempt to describe the cooperativity by the stability of a metastable open system with respect to irreversibility.To treat the evolution of a system weakly coupled to the environment in a kinetic framework,we consider two fluctuating energy levels of different dimensionalities,initial population of one level,reversible transitions of population between the levels,and irreversible depopulation of another level.An average is made over level fluctuations and environment vibrations so that an inter-level transition rate can be obtained accounting for the influences of external control on level position and dimensionality.It is found that the cooperativity of the two-level system is bounded approximately between 0.736 and unity,with the lower bound indicating worsening system stability.     

Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation

Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, "delay" is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of "delay" depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.     

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.     

Multi-Synchronization Caused by Uniform Disorder for Globally Coupled Maps

We investigate the motion of the globally coupled maps （logistic map） driven by uniform disorder. It is shown that this disorder can produce multi-synchronization for the globally coupled chaotic maps studied by us. The disorder determines the synchronized dynamics, leading to the emergence of a wide range of new collective behaviour in which the individual units in isolation are incapable of producing in the absence of the disorder. Our results imply that the disorder can tame the collective motion of the coupled chaotic maps.     

Phase Synchronization in Electrically Coupled Different Neuronal Pacemakers with the Chay Model

We study the phase synchronization in different electrically coupled neuronal pacemakers with the Chay model. The numerical simulation results and the definition of the mean frequency show that phase synchronization is equal to the mean frequency locking. Nearly complete synchronization of different two coupled neuronal pacemakers is also investigated. It is shown that the cross-correlation of the membrane potential variables is suitable to judge the nearly complete synchronization.     

Soliton Solutions of Coupled KdV System from Hirota＇s Bilinear Direct Method

With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.     

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.     

Dynamics of linear discrete systems connected to local, essentially non-linear attachments

The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that non-linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.     

Synchronization in arrays of coupled self-induced friction oscillators

We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.     

The characteristics of nonlinear chaotic dynamics in quantum cellular neural networks

With the polarization of quantum-dot cell and quantum phase serving as state variables, this paper does both theoretical analysis and simulation for the complex nonlinear dynamical behaviour of a three-cell-coupled Quantum Cellular Neural Network （QCNN）, including equilibrium points, bifurcation and chaotic behaviour. Different phenomena, such as quasi-periodic, chaotic and hyper-chaotic states as well as bifurcations are revealed. The system＇s bifurcation and chaotic behaviour under the influence of the different coupling parameters are analysed. And it finds that the unbalanced cells coupled QCNN is easy to cause chaotic oscillation and the system response enters into chaotic state from quasi-periodic state by quasi-period bifurcation; however, the balanced cells coupled QCNN also can be chaotic when coupling parameters is in some region. Additionally, both the unbalanced and balanced cells coupled QCNNs can possess hyper-chaotic behaviour. It provides valuable information about QCNNs for future application in high-parallel signal processing and novel ultra-small chaotic generators.     

Modulation on the collective response behavior by the system size in two-dimensional coupled cell systems

By the intracellular calcium ionic minimal model proposed by Berridge, we investigated the collective response of two-dimensional (N×N) coupled cell systems to the external stimulation using numerical simulation methods. With a coupled intensity fixed and an appropriate coupled cell number chosen, the kinetic system size resonance was discovered. At the same time, it was found that the system size responding to the external stimulation for different coupled intensities transferred too, especially when the coupled intensity increased, the range of the corresponding system size extended. These phenomena illustrate that the coupled cell number and the coupled intensity can play constructive roles in noisy coupled systems, by which the biology system would probably improve its capability to respond to the external stimulation.     

Coupling Strength and System Size Induce Firing Activity of Globally Coupled Neural Network

We investigate how firing activity of globally coupled neural network depends on the coupling strength C and system size N. Network elements are described by space-clamped FitzHugh-Nagumo (SCFHN) neurons with the values of parameters at which no firing activity occurs. It is found that for a given appropriate coupling strength, there is an intermediate range of system size where the firing activity of globally coupled SCFHN neural network is induced and enhanced. On the other hand, for a given intermediate system size level, there exists an optimal value of coupling strength such that the intensity of firing activity reaches its maximum. These phenomena imply that the coupling strength and system size play a vital role in firing activity of neural network.     

The SIMRI project: a versatile and interactive MRI simulator

This paper gives an overview of SIMRI, a new 3D MRI simulator based on the Bloch equation. This simulator proposes an efficient management of the T2* effect, and in a unique simulator integrates most of the simulation features that are offered in different simulators. It takes into account the main static field value and enables realistic simulations of the chemical shift artifact, including off-resonance phenomena. It also simulates the artifacts linked to the static field inhomogeneity like those induced by susceptibility variation within an object. It is implemented in the C language and the MRI sequence programming is done using high level C functions with a simple programming interface. To manage large simulations, the magnetization kernel is implemented in a parallelized way that enables simulation on PC grid architecture. Furthermore, this simulator includes a 1D interactive interface for pedagogic purpose illustrating the magnetization vector motion as well as the MRI contrasts.     

Two mode photon bunching effect as witness of quantum criticality in circuit QED

We suggest a scheme to probe critical phenomena at a quantum phase transition (QPT) using the quantum correlation of two photonic modes simultaneously coupled to a critical system. As an experimentally accessible physical implementation, a circuit QED system is formed by a capacitively coupled Josephson junction qubit array interacting with one superconducting transmission line resonator (TLR). It realizes an Ising chain in the transverse field (ICTF) which interacts with the two magnetic modes propagating in the TLR. We demonstrate that in the vicinity of criticality the originally independent fields tend to display photon bunching effects due to their interaction with the ICTF. Thus, the occurrence of the QPT is reflected by the quantum characteristics of the photonic fields.     

三臂环中的持续电流

利用量子波导理论研究三臂环中的持续电流.结果表明,输运电流存在时,不含磁场且上、下臂等长的三臂环中仍可以有持续电流出现,而且上臂和下臂中的持续电流是相同的.三臂环的各臂长不等时,三个臂中的持续电流各不相同.我们还发现,即使三臂环和单环的上、下臂比值一样,两个环中的持续电流也明显不同.