He Shaobo, Rajagopal Karthikeyan, Karthikeyan Anitha, Srinivasan Ashokkumar
School of Physics and Electronics, Central South University, Changsha, 410083 China.
Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India.
Cogn Neurodyn. 2023 Feb;17(1):301-310. doi: 10.1007/s11571-022-09806-1. Epub 2022 May 3.
Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network.
The online version contains supplementary material available at 10.1007/s11571-022-09806-1.
许多著名的神经元模型是具有复杂数学定义的连续时间系统。文献表明，离散数学模型可以有效复制神经元的完整动力学行为，且复杂度大幅降低。因此，我们提出了一种新的离散神经元模型，它源自于休伯 - 布劳恩神经元，除离子通道电流外，还增加了两个额外的缓慢且低于阈值的电流。我们还引入了温度依赖型离子通道来研究其对神经元放电模式的影响。通过分岔和李雅普诺夫指数，我们展示了离散模型的混沌和周期区域。为了进一步研究神经元模型的复杂性，我们使用了样本熵算法。虽然单个神经元分析能让我们了解其动力学特性，但决定神经元整体行为模式的是集体行为。因此，我们研究了离散神经元模型在单层和两层网络中的时空行为。我们将障碍物视为改变网络中神经元兴奋性的一个重要因素。文献表明，螺旋波作为起搏器，通过产生相干共振行为，在突破大脑静止区域方面可以发挥积极作用。因此，我们对研究网络中诱导产生的螺旋波感兴趣。在这种情况下，当引入障碍物时，波的传播会受到干扰，我们可以看到多次波的重新进入和螺旋波。在两层网络中，当仅在一层设置障碍物并对有障碍物的层施加刺激时，尽管另一层未接触障碍物，但两层都会出现波的重新进入。但是当两层都插入障碍物并对两层都施加刺激时，它们的行为就像独立的层，没有耦合效应。在两层网络中，刺激在网络的时空动力学中起着重要作用。
在线版本包含可在10.1007/s11571 - 022 - 09806 - 1获取的补充材料。
