【作者】 谢勇；

【Author】 Yong Xie (MOE Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P R China)

【机构】 西安交通大学航天航空学院强度与振动教育部重点实验室；

【摘要】 提出一种通过分岔控制改变神经元兴奋性类型的方法。采用一个基于washout滤波器的动态反馈控制实现对一个二维的Hindmarsh-Rose类的模型神经元的分岔动力学控制。这一模型神经元从静息态到峰放电态跨越一个不变圆上鞍结分岔(saddle-node on invariant circle,SNIC),呈现出第一类兴奋性。在该SNIC分岔前所期望的参数值处产生一个Hopf分岔,然后通过选择适当的控制器参数调节Hopf分岔的临界性。这样,模型神经元就呈现为第二类兴奋性,因此神经元兴奋性就从第一类改变成第二类。在这个控制器中,线性控制增益决定着Hopf分岔的位置,而非线性增益决定着Hopf分岔的临界性。更多还原

【Abstract】 This paper proposes an approach to changing the types of neuronal excitability via bifurcation control. A washout filter-aided dynamic feedback controller is introduced to bifurcation dynamics of a two-dimensional Hindmarsh-Rose type model neuron, which shows a saddle-node on invariant circle (SNIC) bifurcation from quiescence to periodic spiking and then exhibits Type I excitability. At first, a Hopf bifurcation is created at a desired parameter value before the SNIC bifurcation occurs, and then the criticality of the created Hopf bifurcation is regulated by choosing appropriate values of the controller parameters. In this manner, the model neuron starts to show Type II excitability. Therefore, the type of neuronal excitability is transformed from Type I excitability to Type II excitability for the model neuron via the washout filter-aided dynamic feedback controller. In such a controller, the linear control gain determines the location of the Hopf bifurcation, and the nonlinear control gain underlies the criticality of the created Hopf bifurcation.更多还原