Yanqiu Che

Topology identification of uncertain nonlinearly coupled complex networks with delays based on anticipatory synchronization

This paper presents an adaptive anticipatory synchronization based method for simultaneous identification of topology and parameters of uncertain nonlinearly coupled complex dynamical networks with time delays. An adaptive controller is proposed, based on Lyapunov stability theorem and Barbǎlats Lemma, to guarantee the stability of the anticipatory synchronization manifold between drive and response networks. Meanwhile, not only the identification criteria of network topology and system parameters are obtained but also the anticipatory time is identified. Numerical simulation results illustrate the effectiveness of the proposed method.

Bifurcations in the Hodgkin-Huxley model exposed to DC electric fields

Diverse behaviors of the original Hodgkin-Huxley (HH) model, depending on the parameter values, have been studied extensively. This paper proposes modified HH equations exposed to externally applied extremely low frequency (ELF) electric fields. We investigate the effect of the DC electric fields on the dynamics of the modified HH model using bifurcation analysis. The obtained bifurcation sets partition the two dimensional parameter space, representing intensity of externally applied DC current and trans-membrane voltage induced by external DC electric fields, in terms of the qualitatively different behaviors of the HH model. Thus the neuronal information encodes the stimulus information, and vice versa. We also illustrate that the multi-stability phenomena in the HH model are associated with Hopf and double cycle bifurcations.

Parameter estimation of the FitzHugh-Nagumo model using noisy measurements for membrane potential.

This paper proposes an identification method to estimate the parameters of the FitzHugh-Nagumo (FHN) model for a neuron using noisy measurements available from a voltage-clamp experiment. By eliminating an unmeasurable recovery variable from the FHN model, a parametric second order ordinary differential equation for the only measurable membrane potential variable can be obtained. In the presence of the measurement noise, a simple least squares method is employed to estimate the associated parameters involved in the FHN model. Although the available measurements for the membrane potential are contaminated with noises, the proposed identification method aided by wavelet denoising can also give the FHN model parameters with satisfactory accuracy. Finally, two simulation examples demonstrate the effectiveness of the proposed method.

An ephaptic transmission model of CA3 pyramidal cells: an investigation into electric field effects

Extracellular electric fields existing throughout the living brain affect the neural coding and information processing via ephaptic transmission, independent of synapses. A two-compartment whole field effect model (WFEM) of pyramidal neurons embedded within a resistive array which simulates the extracellular medium i.e. ephapse is developed to study the effects of electric field on neuronal behaviors. We derive the two linearized filed effect models (LFEM-1 and LFEM-2) from WFEM at the stable resting state. Through matching these simplified models to the subthreshold membrane response in experiments of the resting pyramidal cells exposed to applied electric fields, we not only verify our proposed model’s validity but also found the key parameters which dominate subthreshold frequency response characteristic. Moreover, we find and give its underlying biophysical mechanism that the unsymmetrical properties of active ion channels results in the very different low-frequency response of somatic and dendritic compartments. Following, WFEM is used to investigate both direct-current (DC) and alternating-current field effect on the neural firing patterns by bifurcation analyses. We present that DC electric field could modulate neuronal excitability, with the positive field improving the excitability, the modest negative field suppressing the excitability, but interestingly, the larger negative field re-exciting the neuron back into spiking behavior. The neuron exposed to the sinusoidal electric field exhibits abundant firing patterns sensitive to the input frequency and intensity. In addition, the electrical properties of ephapse can modulate the efficacy of field effect. Our simulated results are qualitatively in line with the relevant experimental results and can explain some experimental phenomena. Furthermore, they are helpful to provide the predictions which can be tested in future experiments.

Synchronization of inhibitory coupled Hindmarsh-Rose neurons via adaptive sliding mode control

This paper presents an adaptive neural network (NN) sliding mode control for synchronization of inhibitory coupled Hindmarsh-Rose (HR) neurons. A single HR neuron may exhibit spike-burst chaotic behaviors. Inhibitory coupling makes two HR neurons behaves in anti-phase quasi-synchronization mode. We first derive the sliding mode controller via active control strategy. Then, a simple radial basis function (RBF) NN is designed to approximate the uncertain nonlinear part of the error dynamical system which has been assumed to be available in the active control. The weights of the NN are tuned on-line based on the sliding mode reaching law. According to the Lyapunov stability theory, the stability of the closed-loop error system is guaranteed. Synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.

Effects of couplings on the optimal desynchronizing control of neuronal networks

Excessive synchronization of neurons in the basal ganglia of the brain is one of the hallmarks for Parkinsons disease (PD). It has been proven that the high-frequency deep brain stimulation (DBS) was an effective treatment for PD patients, and it could alleviate the symptoms of PD by mitigating the pathological synchronous oscillations of neurons. To reduce risks of excessive high-frequency stimulus and improve the DBS treatment, researchers have paid much attention to the optimization strategies of DBS based on neuronal network models. However, the influence of neuronal network models on the control performance has been neglected which significantly affected this optimization. This paper investigated the effects of neuronal network models on the optimal desynchronizing control of synchronized neurons, which was done by applying the discrete time dynamic programming method to reduced phase models for neurons. Numerical simulations show that the coupling types and strengths as well as connection topologies of neuronal networks influence the desynchronizing results greatly. Such as, the neuronal networks with chemical synaptic couplings are more easily to be desynchronized than those with electrotonic couplings, and the networks containing symmetry are very difficult to be desynchronized. This research can contribute to the development and application of the optimal DBS control strategies.

Endogenous field feedback promotes the detectability for exogenous electric signal in the hybrid coupled population

This paper presents the endogenous electric field in chemical or electrical synaptic coupled networks, aiming to study the role of endogenous field feedback in the signal propagation in neural systems. It shows that the feedback of endogenous fields to network activities can reduce the required energy of the noise and enhance the transmission of input signals in hybrid coupled populations. As a common and important nonsynaptic interactive method among neurons, particularly, the endogenous filed feedback can not only promote the detectability of exogenous weak signal in hybrid coupled neural population but also enhance the robustness of the detectability against noise. Furthermore, with the increasing of field coupling strengths, the endogenous field feedback is conductive to the stochastic resonance by facilitating the transition of cluster activities from the no spiking to spiking regions. Distinct from synaptic coupling, the endogenous field feedback can play a role as internal driving force to boost the population activities, which is similar to the noise. Thus, it can help to transmit exogenous weak signals within the network in the absence of noise drive via the stochastic-like resonance.

Effects of topologies on signal propagation in feedforward networks

We systematically investigate the effects of topologies on signal propagation in feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. FFNs with different topological structures are constructed with same number of both in-degrees and out-degrees in each layer and given the same input signal. The propagation of firing patterns and firing rates are found to be affected by the distribution of neuron connections in the FFNs. Synchronous firing patterns emerge in the later layers of FFNs with identical, uniform, and exponential degree distributions, but the number of synchronous spike trains in the output layers of the three topologies obviously differs from one another. The firing rates in the output layers of the three FFNs can be ordered from high to low according to their topological structures as exponential, uniform, and identical distributions, respectively. Interestingly, the sequence of spiking regularity in the output layers of the three FFNs is consistent with the firing rates, but their firing synchronization is in the opposite order. In summary, the node degree is an important factor that can dramatically influence the neuronal network activity.

The estimation of neurotransmitter release probability in feedforward neuronal network based on adaptive synchronization

In this paper, we proposed a new approach to estimate unknown parameters and topology of a neuronal network based on the adaptive synchronization control scheme. A virtual neuronal network is constructed as an observer to track the membrane potential of the corresponding neurons in the original network. When they achieve synchronization, the unknown parameters and topology of the original network are obtained. The method is applied to estimate the real-time status of the connection in the feedforward network and the neurotransmitter release probability of unreliable synapses is obtained by statistic computation. Numerical simulations are also performed to demonstrate the effectiveness of the proposed adaptive controller. The obtained results may have important implications in system identification in neural science.

Effect of delay on the synchronization of weakly coupled neurons via gap junctions

Weak electrical coupling connections are ubiquitous in neuronal system. In this paper, we examine the effect of time delays on the synchronization properties of the weakly coupled neuronal oscillators by means of phase-model reduction. The bifurcation analysis clarifies how the time delays affect the existence and stability of in-phase, anti-phase and out of phase synchronization states. The results show that time delay can promote synchronization in an efficient way.