Autapse is a type of synapse that connects axon and dendrites of the same neuron, and the effect is often detected by close-loop feedback in axonal action potentials to the owned dendritic tree. An artificial autapse was introduced into the Hindmarsh-Rose neuron model, and a regular network was designed to detect the regular pattern formation induced by autapse. It was found that target wave emerged in the network even when only a single autapse was considered. By increasing the(autapse density) number of neurons with autapse, for example, a regular area(2×2, 3×3, 4×4, 5×5 neurons) under autapse induced target wave by selecting the feedback gain and time-delay in autapse. Spiral waves were also observed under optimized feedback gain and time delay in autapses because of coherence-like resonance in the network induced by some electric autapses connected to some neurons. This confirmed that the electric autapse has a critical role in exciting and regulating the collective behaviors of neurons by generating stable regular waves(target waves, spiral waves) in the network. The wave length of the induced travelling wave(target wave, spiral wave), because of local effect of autapse, was also calculated to understand the waveprofile in the network of neurons.
The probability of long-range connection among neurons could be changeable in biological neuronal networks. In this paper, the probability of long-range connection between neurons is not fixed at a constant but varies in a numerical region (≤p0 ), and then the collective behaviors of neurons are detected. A statistical factor in the two-dimensional space is used to detect the phase transition and robustness of spiral wave in the active network of neurons. It is found that the development of spatiotem-poral pattern depends on the numerical region (≤p0 ) for the probability of long-range connection. Coherence resonance-like behavior is observed due to the fluctuation in the long-range probability. Spiral waves emerge to occupy the network of neurons under an optimized probability of long-range connection, and it shows certain robustness in weak channel noise.
The electric activities of neurons could be changed when ion channel block occurs in the neurons.External forcing currents with diversity are imposed on the regular network of Hodgkin-Huxley(HH) neuron,and target waves are induced to occupy the network.The forcing current I1 is imposed on neurons in a local region with m 0 ×m 0 nodes in the network,neurons in other nodes are imposed with another forcing current I2.Target wave could be developed to occupy the network when the gradient forcing current(I1-I2) exceeds certain threshold,and the formation of target wave is independent of the selection of boundary condition.It is also found that the developed target wave can decrease the negative effect of ion channel block and suppress the spiral wave,and thus channel noise is also considered.The potential mechanism of formation of target wave could be that the gradient forcing current(I1-I2) generates quasi-periodical signal in local area,and the propagation of quasi-periodical signal induces target-like wave due to mutual coupling among neurons in the network.
Autapse connected to the neuron can change the electric activity of neuron. The effect of autapse on neuronal activity is often described by adding an additive forcing current along a close loop, which is described by a time-delayed feedback on the membrane potential. Neuron often responds to electric autapse forcing sensitively and quickly, while the chemical autapse changes the electric activity of neuron slowly. By applying external forcing, a shift transition of electric activity can be more easily induced by the electric autapse than the chemical autapse. Our results confirm that chemical autapse can enhance and/or suppress the transition of electric activity with excitable or inhibitory type driven by electric autapse, vice versa. It indicates that an appropriate switch-off-on for autapse can make the neuron give different types of response to external forcing. Particularly, cooperation and competition between chemical and electric autapse help neuron response to external forcing in the most reliable way.
The nervous system is composed of a large number of neurons, and the electrical activities of neurons can present multiple modes during the signal transmission between neurons by changing intrinsic bifurcation parameters or under appropriate external forcing. In this review, the dynamics for neuron, neuronal network is introduced, for example, the mode transition in electrical activity, functional role of autapse connection, bifurcation verification in biological experiments, interaction between neuron and astrocyte, noise effect, coherence resonance, pattern formation and selection in network of neurons. Finally, some open problems in this field such as electromagnetic radiation on electrical activities of neuron, energy consumption in neurons are presented.
