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.     

Collective behaviors of suprachiasm nucleus neurons under different light–dark cycles

The principal circadian clock in the suprachiasm nucleus(SCN) regulates the circadian rhythm of physiological and behavioral activities of mammals. Except for the normal function of the circadian rhythm, the ensemble of SCN neurons may show two collective behaviors, i.e., a free running period in the absence of a light–dark cycle and an entrainment ability to an external T cycle. Experiments show that both the free running periods and the entrainment ranges may vary from one species to another and can be seriously influenced by the coupling among the SCN neurons. We here review the recent progress on how the heterogeneous couplings influence these two collective behaviors. We will show that in the case of homogeneous coupling, the free running period increases monotonically while the entrainment range decreases monotonically with the increase of the coupling strength. While in the case of heterogenous coupling, the dispersion of the coupling strength plays a crucial role. It has been found that the free running period decreases with the increase of the dispersion while the entrainment ability is enhanced by the dispersion. These findings provide new insights into the mechanism of the circadian clock in the SCN.     

Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge-qubits interacting with an LC-resonator.It is found that when the initial states of the two qubits are prepared in a given superposition excited state,the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits.With the variation of the coupling strength,the evolution of the entanglement entropy of the system forms some structures,especially the periodically bistable properties,which are the first discovered for such a system to our knowledge.It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits,some novel ’collective oscillations’ of the relative entropy are found for the system.     

Spiking Regularity and Coherence in Complex Hodgkin-Huxley Neuron Networks

We study the effects of the strength of coupling between neurons on the spiking regularity and coherence in a complex network with randomly connected Hodgkin-Huxley neurons driven by colored noise. It is found that for the given topology realization and colored noise correlation time, there exists an optimal strength of coupling, at which the spiking regularity of the network reaches the best level, Moreover, when the temporal regularity reaches the best level, the spatial coherence of the system has already increased to a relatively high level. In addition, for the given number of neurons and noise correlation time, the values of average regularity and spatial coherence at the optimal strength of coupling are nearly independent of the topology realization. Furthermore, there exists an optimal value of colored noise correlation time at which the spiking regularity can reach its best level. These results may be helpful for understanding of the real neuron world.     

The synchronization of FitzHugh--Nagumo neuron network coupled by gap junction

It is well known that the strong coupling can synchronize a network of nonlinear oscillators. Synchronization provides the basis of the remarkable computational performance of the brain. In this paper the FitzHugh-Nagumo neuron network is constructed. The dependence of the synchronization on the coupling strength, the noise intensity and the size of the neuron network has been discussed. The results indicate that the coupling among neurons works to improve the synchronization, and noise increases the neuron random dynamics and the local fluctuations; the larger the size of network, the worse the synchronization. The dependence of the synchronization on the strength of the electric synapse coupling and chemical synapse coupling has also been discussed, which proves that electric synapse coupling can enhance the synchronization of the neuron network largely.     

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.     

Non-Markovian speedup dynamics control of the damped Jaynes-Cummings model with detuning

For a two-level atom in a lossy cavity, a scheme to manipulate the non-Markovian speedup dynamics has been proposed in the controllable environment(the lossy cavity field). We mainly focus on the effects of the qubit-cavity detuning ? and the qubit-cavity coupling strength κ on the non-Markovian speedup evolution of an open system. By controlling the environment, i.e., tuning ? and κ, two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved. Furthermore, it is clearly found that increasing the coupling strength κ or detuning ? in some cases can make the environmental non-Markovianity stronger and hence can lead to faster evolution of the open system.     

Coherence effects in S/I/N/I/FS tunnel junctions

The dc Josephson effect in superconductor / insulator / normal metal / insulator/ferromagnetic superconductor junctions has been studied. We calculate the de Josephson current based on the Bogoliubov de Gennes equation. The Josephson current is derived as a function of exchange field in ferromagnetic superconductor, normal metal thickness and insulating barrier strength. It is found that there exists an oscillation relation between the critical Josephson current and the normal metal thickness. The oscillation amplitude decreases as the thickness of the normal metal increases or the exchange field augments.[第一段]     

Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

We analyze the energy aspects of single and coupled Hindmarsh–Rose(HR) neuron models with a quadratic flux controlled memristor. The energy function for HR neuron with memristor has been derived and the dynamics have been analyzed in the presence of various external stimuli. We found that the bursting mode of the system changes with external forcing. The negative feedback in Hamilton energy function effectively stabilizes the chaotic trajectories and controls the phase space. The Lyapunov exponents have been plotted to verify the stabilization of trajectories. The energy aspects during the synchronous dynamics of electrically coupled neurons have been analyzed. As the coupling strength increases, the average energy fluctuates and stabilizes at the point of synchronization. When the neurons are coupled via chemical synapse,the average energy variations show three important regimes: a fluctuating regime corresponding to the desynchronized, a stable region indicating synchronized and a linearly increasing regime corresponding to the amplitude death states have been observed. The synchronization transitions are verified by plotting the transverse Lyapunov exponents. The proposed method has a large number of applications in controlling coupled chaotic systems and in analyzing the energy change during various metabolic processes.     

Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise

This paper investigates the stochastic resonance （SR） phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.