New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay

This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results. Supported by the National Natural Science Foundation of China (Grant Nos. 60534010, 60728307, 60774048, 60774093), the Program for Cheung Kong Scholars and Innovative Research Groups of China (Grant No. 60521003) and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z183), China Postdoctoral Sciencer Foundation (Grant No. 20080431150), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200801451096)     

VRLA蓄电池浮充电压均一性的探讨

阐述了ＶＲＬＡ蓄电池浮充过程中电压均一性与蓄电池密封反应效率、容量、杂质、浮充电压设置及连接件的关系,相应地提出了生产过程中对以上因素的解决方法。     

Absolute stabilization of singular systems with ferromagnetic hysteresis nonlinearity

This paper is concerned with the absolute stabilization problem of a class of singular systems with feedback connected ferromagnetic hysteresis nonlinearities. Firstly, a novel differential-integral loop transformation framework is developed to achieve an augmented singular system model. Secondly, by constructing a new passive output derivative operator of hysteresis nonlinearity and establishing the bound condition of the solution of ferromagnetic hysteresis model, the equivalent absolute stability criterion of singular systems with hysteresis feedback is derived based on KYP method and LMIs technique. Furthermore, the strict LMIs conditions for absolute stabilization are obtained, which can easily be checked by the LMI toolbox in MATLAB. Finally, two examples are given to illustrate the effectiveness of the proposed method.     

Stochastic dynamics of conduction failure of action potential along nerve fiber with Hopf bifurcation

Action potentials can be induced by external electronic impulsive stimulations applied at one end of the unmyelinated fibers(C-fibers), while some action potentials fail to conduct to the other end of the fiber when the stimulation frequency becomes high. Such a phenomenon is called as conduction failure, which was observed in the biological experiments and related to the painful diabetic neuropathy, inflammation, and trauma in the previous studies. On-off firing pattern was recorded from the fiber when conduction failure happened. In the present study, the diffusion Hodgkin-Huxley(HH) model with resting state near a Hopf bifurcation is adopted to simulate the experimental observations. When the periodic electrical pulses with high frequency are applied to one end of the fiber described by the deterministic HH model, conduction failure and the corresponding firing patterns different from the on-off firing pattern are simulated. When noise is introduced to form the stochastic HH model, the firing pattern corresponding to conduction failure becomes the on-off firing pattern, which is characterised by transition behaviors between on-phase(continuous action potentials) and off-phase(a long quiescent state) and large variations in the durations of both phases. Furthermore, the increase of potassium conductance can enhance the conduction failure degree, which closely matches those observed in the experiment and is suggested to be related to the reduction of pain signals. The results show that noise is an important factor to evoke the on-off firing pattern, reveal the functional capability in the pain signals propagation along C-fiber,and present a possible measure for the treatment of chronic pain.     

Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker

Changes of neural firing patterns and transitions between firing patterns induced by the introduction of external stimulation or adjustment of biological parameter have been demonstrated to play key roles in information coding.In this paper,bifurcation processes of bursting patterns were observed from an experimental neural pacemaker,through the adjustment of potassium parameter including ion concentration and calcium-dependent channel conductance.The adjustment of calcium-dependent potassium channel conductance was achieved by changing the extracellular tetraethylammonium concentration.The deterministic dynamics of chaotic bursting patterns induced by period-doubling bifurcation and intermittency,and lying between two periodic bursting patterns in a period-adding bifurcation process was investigated with a nonlinear prediction method.The bifurcations included period-doubling and period-adding bifurcations of bursting patterns.The experimental bifurcations and chaos closely matched those previously simulated in the theoretical neuronal model by adjusting potassium parameter,which demonstrated the simulation results of the theoretical model.The experimental results indicate that the potassium concentration and conductance of calcium-dependent potassium channel can induce bifurcations of the neural firing patterns.The potential role of these bifurcation structures in neural information coding mechanism is discussed.     

Spatiotemporal dynamics in a network composed of neurons with different excitabilities and excitatory coupling

Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves observed in the experiment, the spatiotemporal patterns are investigated in a network composed of neurons with type I and II excitabilities and excitatory coupling. Spiral waves emerge when the percentage (p) of neurons with type I excitability in the network is at middle levels, which is dependent on the coupling strength. Compared with other spatial patterns which appear at different p values, spiral waves exhibit optimal spatial correlation at a certain spatial frequency, implying the occurrence of spatial coherence resonance-like phenomenon. Some dynamical characteristics of the network such as mean firing frequency and synchronous degree can be well interpreted with distinct properties between type I excitability and type II excitability. The results not only identify dynamics of spiral waves in neuronal networks composed of neurons with different excitabilities, but also are helpful to understanding the emergence of spiral waves observed in the biological experiment.     

The nonlinear mechanism for the same responses of neuronal bursting to opposite self-feedback modulations of autapse

In the traditional viewpoint,inhibitory and excitatory effects always induce opposite responses.In the present study,the enhanced bursting activities induced by excitatory autapses,which are consistent with the recent experimental observations,and those induced by inhibitory autapses,which is a paradoxical phenomenon,were simulated using the Chay model.The same bifurcations and different ionic currents for the same responses were acquired with fast-slow variable dissection and current decomposition,respectively.As the inhibitory or excitatory autaptic conductance increased,the ending phase of the burst related to a homoclinic bifurcation of the fast subsystem changed to widen the burst duration to contain more spikes,which was induced by an elevated minimal potential(V_(min)) of spiking of the fast subsystem.Larger inhibitory and excitatory autaptic conductances induced smaller and larger maximal potentials(V_(max)) of spiking,respectively.During the downstroke,a weaker potassium current induced by the smaller V_(max) played a dominant role for the inhibitory autapse,and the stronger potassium current induced by the larger V_(max) became weaker due to the opposite autaptic current of the excitatory autapse,which induced the V_(min) elevated.The results present the nonlinear and biophysical mechanisms of the same responses to opposite effects,which extends nonlinear dynamics knowledge and provides potential modulation measures for the nervous system.