摘要
神经元对信息的处理和加工是神经元集群共同完成的,因此神经元集群的运动模式信息的传递是非常重要的。单个神经元不能完成对连续峰放电的时间序列进行编码,而神经元集群能以同步方式反映出共同的突触电流。同步广泛存在于不同的生物系统中,但是,并非所有的同步形式对生物系统是有利的,例如手的颤抖、帕金森综合症和癫痫病等都是由神经元的病态同步产生的。因此,发现各种促进和抑制耦合神经元的同步方法是非常重要的,这样才能发现有效消除帕金森综合症和癫痫病的方法和帮助人认识人脑的整个功能。近年来,利用非线性动力学的理论和方法来研究神经元的同步与去同步为一个热点课题。本文研究了Hadmarsh-Rose神经元的同步以及去同步的问题。全文的内容安排如下：
第一章主要介绍了神经元的基本知识、Hindmarsh-Rose神经元模型和几种常见的混沌同步
第二章采用Hindmarsh-Rose(?)(?)经元模型,研究了两个神经元系统的单变量驱动响应混合同步问题,提出反馈控制与自适应控制相结合的同步策略,从理论上分析了该同步方案的可行性,数值模拟结果表明,该同步方案能使部分变量达到反同步,使其它变量达到同步,即只需要单个变量的驱动就能实现两个混沌神经元的同步和反同步,当采用两个变量驱动时实现了两个混沌神经元的完全反同步.
第三章研究了二维点阵上的Hindmarsh-Rose神经网络的同步,采用延迟全局耦合,延迟时间长度与神经元之间的空间距离成正比。我们发现延时总是干扰网络的同步,当耦合强度和单位距离的延迟时间长度(或者放大因子)足够大时,在神经元中观察到由于延迟导致的异常振荡现象,而且在点阵对称点上的神经元的振荡是反相的,从而大的耦合强度和大的放大因子总是导致网络的去同步,在一定条件下观察到全局同步和间歇全局同步。对产生这些现象的物理机制作了解释。
The information processing is completed by neuronal colony in neuronal system. So the movement pattern of neuronal colony is very important for the transmission of information. A single neuron can thus not implement the temporal codes of the neuron spike trains. However, the neuronal colony can give the common synapse electric current by the synchronous mode. Synchronizations widely exist in the different biological systems. Synchronization is not always desirable. For example, synchronization of individual neurons leads to the emergence of pathological rhythmic brain activity in Parkinson's disease, essential tremor, and epilepsies. Therefore, it is important to find various methods to suppress or facilitate the synchronization of coupled neuronal systems. These can discover the methods which can effectively eliminate the Parkinson syndrome and the insane epilepsy and help people to know the entire function of human brain. Recently, the research of synchronization and de-synchronization in the coupled neurons bases on theory of nonlinear dynamics become a hot topic. Synchronization and de-synchronization of coupled Hindmarsh-Rose neurons is investigated in this paper. The paper is organized as follows:
The first chapter mainly introduces the basic theory of neurons, Hindmarsh-Rose neuron model and the common kinds of chaos synchronization.
In the second chapter, the hybrid synchronization of two neurons described by Hindmarsh-Rose neuron model via single variable drive-response control is investigated. The synchronization strategy which applies feedback and adaptive control is proposed. The feasibility of the synchronization method is analyzed. The numerical results show that the synchronization method can lead to anti-synchronization of partial variables while it causes synchronization of other variables, namely anti-synchronization and synchronization of two chaotic neurons can be achieved by single variable control. We also find that the anti-synchronization of two chaotic neurons can be achieved when two control variable are applied.
In the third chapter, the synchronization is investigated in a two dimensional Hindmarsh-Rose neuronal network by introducing a global coupling scheme with time delay, where the length of delay time is proportional to the spatial distance between neurons. We find that the time delay always disturbs synchronization of the networks. When both the coupling strength and length of time delay per unit distance (i.e., enlargement factor) are large enough, abnormal oscillations of neurons are observed due to the time delay. Furthermore, the abnormal oscillations of the symmetrical neurons form inverse phase so that the large coupling strength and enlargement factor lead to the de-synchronization of the neuronal network. The complete and intermittently complete synchronization of the neuronal network are observed for the right choice of parameter. The physical mechanism underlying these phenomena is analyzed.
引文
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