电磁辐射下神经元的建模及其动力学分析

发布时间：2018-04-23 23:23

本文选题：Hindmarsh-Rose神经元 + 磁通　；参考：《兰州理工大学》2017年硕士论文

【摘要】：在神经系统中,神经元的电活动行为依赖于复杂的电生理条件,这表明在神经系统中可以检测到复杂的电磁场分布。根据电磁感应定律,由于神经系统内部生物电的影响,使得每个神经元的电活行为有所改变。所以当神经元出现集体的电活动行为或者信号在大量神经元之间传播时,就应该考虑内部电磁场的波动和穿过细胞膜的磁通的作用。基于传统的Hindmarsh-Rose神经元模型引入一维磁通变量,建立起一个四变量的神经元模型用来描述神经元中的电磁感应现象。在这个新模型中,考虑到了磁通对膜电位的作用,在膜电位变量加上记忆电流项。通过改变初始状态研究改造模型的动力学特性,可以观察到多模式的放电活动,这表明了神经系统具有记忆效应。其次用改进的神经元模型研究电磁感应对神经元动力学行为的影响,当不同强度的电磁辐射施加在神经元上时,可以检测神经元中电活动的模式转换。改进后的神经元模型具有更多的分岔参数而且电活动的模式可以在很大的参数范围内进行选择。我们发现电磁辐射可以激发静息态的神经元,也可以抑制神经元中的电活动,重要的是发现多模式的电活动可以交替出现,并且这些结果与生物实验一致。基于改进的神经元模型,通过进行磁通耦合,在神经元模型上研究其相位同步。时变电磁场的效应由磁通量来描述,电磁场的耦合也通过磁通量的交换来实现。神经元之间通过磁通耦合可以实现完美的相位同步。通过计算Lyapunov指数和Lyapunov维度来检测混沌时间序列的相位同步。最后基于一个忆阻器网络,研究其网络同步行为。网络可以通过选择恰当的耦合强度达到完全同步。然后改变网络分岔参数,即让网络参数从以前的值切换至另一个值,观测网络同步行为发现:参数的变化使得网络同步遭到很大程度的破坏;损伤面积的大小依赖于参数损坏和变形程度以及破坏的扩散周期。
[Abstract]:In the nervous system, the electrical activity of neurons depends on complex electrophysiological conditions, which indicates that complex electromagnetic fields can be detected in the nervous system. According to the law of electromagnetic induction, the electrical activity of each neuron is changed due to the effect of bioelectricity in the nervous system. Therefore, when the neurons exhibit collective electrical activity or the signal propagates between a large number of neurons, the fluctuation of the internal electromagnetic field and the effect of the magnetic flux passing through the cell membrane should be taken into account. Based on the traditional Hindmarsh-Rose neuron model, a four-variable neuron model was established to describe the electromagnetic induction phenomenon in neurons by introducing one-dimensional flux variables. In this new model, considering the effect of magnetic flux on membrane potential, a memory current term is added to the membrane potential variable. By changing the dynamic characteristics of the modified model, the multi-mode discharge activity can be observed, which indicates that the nervous system has memory effect. Secondly, the effect of electromagnetic induction on neuronal dynamic behavior is studied by using the improved neuron model. When the electromagnetic radiation of different intensity is applied to the neuron, the mode conversion of electrical activity in the neuron can be detected. The improved neuron model has more bifurcation parameters and the mode of electrical activity can be selected in a wide range of parameters. We find that electromagnetic radiation can excite resting neurons and inhibit electrical activity in neurons. It is important to find that multi-mode electrical activity can occur alternately and these results are consistent with biological experiments. Based on the improved neuron model, the phase synchronization is studied on the neuron model by magnetic flux coupling. The effect of time-varying electromagnetic field is described by magnetic flux, and the coupling of electromagnetic field is also realized by the exchange of magnetic flux. Perfect phase synchronization can be achieved by magnetic flux coupling between neurons. The phase synchronization of chaotic time series is detected by calculating Lyapunov exponent and Lyapunov dimension. Finally, based on a resistive network, the synchronization behavior of the network is studied. The network can be fully synchronized by selecting the appropriate coupling strength. Then changing the network bifurcation parameters, that is, switching the network parameters from the previous value to another value, and observing the network synchronization behavior, it is found that the network synchronization is destroyed to a large extent by the change of the parameters; The size of damage area depends on the degree of damage and deformation and the diffusion period of damage.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R338;O441

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