神经元模型的分岔分析与控制

发布时间：2018-09-07 10:43

【摘要】：神经系统是一个网络系统,这个网络可以控制和调节我们身体所有的生理过程。神经系统控制和调节的崩溃会导致潜在生理机制的异常和混乱从而导致出现许多神经疾病,例如,癫痫,老年痴呆症,帕金森病以及精神分裂症等。从非线性动力系统的角度来看,这些疾病可以认为是由描述神经元系统的相关非线性方程组的一个或多个调节参数的值的改变所诱导的分岔引起的。因此,深入研究分岔的产生及控制对这些动态疾病的诊断和治疗有潜在的应用。基于Washout滤波的动态状态反馈控制器已被应用于多种非线性动力学模型。本文以Morris-Lecar(ML)模型为研究对象,利用非线性动力学理论和方法来分析该模型产生分岔的机理并利用Washout滤波器来控制其分岔。该控制器包含一个线性项和一个非线性项,研究表明该控制器的线性项决定Hopf分岔点的位置,避免分岔点出现在一些确定的外加应用电流区域,而非线性项可以调节Hopf分岔点的稳定性。本文接着分析了外加应用电流,线性控制增益,非线性控制增益和滤波器时间常数的倒数之间的关系。通过这些关系,我们可以选择合适的参数值以达到我们的控制目标。本文还分析了神经元系统可控参数与外加应用电流的关系,仅通过调节可控参数的参数值而不加入任何控制,我们可以改变Hopf分岔点的位置,甚至可以改变神经元的兴奋类型。相比加入控制器来改变这些特性,这种方法不会因增加系统的维数而使系统变复杂。以上分析和控制的结果有助于揭示某些神经疾病的致病机理,为这些神经疾病的预防和治疗提供一定的理论支持,在临床医学应用上有一定的指导意义。
[Abstract]:The nervous system is a network that controls and regulates all the physical processes of our body. The breakdown of nervous system control and regulation can lead to abnormalities and confusion of underlying physiological mechanisms, leading to many neurological diseases, such as epilepsy, Alzheimer's disease, Parkinson's disease and schizophrenia. From the point of view of nonlinear dynamical system, these diseases can be thought to be caused by the bifurcation induced by the change of the value of one or more regulating parameters of the related nonlinear equations describing the neuronal system. Therefore, further research on the generation and control of bifurcation has potential applications in the diagnosis and treatment of these dynamic diseases. Dynamic state feedback controller based on Washout filter has been applied to many nonlinear dynamic models. In this paper, Morris-Lecar (ML) model is taken as the research object. The mechanism of bifurcation is analyzed by nonlinear dynamics theory and method, and the bifurcation is controlled by Washout filter. The controller consists of a linear term and a nonlinear term. It is shown that the linear term of the controller determines the position of the Hopf bifurcation point and avoids the occurrence of the bifurcation point in certain applied current regions. The nonlinear term can adjust the stability of Hopf bifurcation point. Then the relationship between applied current, linear control gain, nonlinear control gain and the reciprocal of filter time constant is analyzed. Through these relationships, we can select the appropriate parameter values to achieve our control objectives. This paper also analyzes the relationship between the controllable parameters of the neuron system and the applied current. By adjusting the parameters of the controllable parameters without adding any control, we can change the position of the Hopf bifurcation point and even the excitation type of the neuron. Compared with adding a controller to change these characteristics, this method does not complicate the system by increasing the dimension of the system. The results of above analysis and control are helpful to reveal the pathogenic mechanism of some neurological diseases, and provide certain theoretical support for the prevention and treatment of these neurological diseases, and have certain guiding significance in clinical application.
【学位授予单位】：长江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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