论文标题
修饰的theta模型的神经元种群动力学的分叉：向宏观伽马振荡过渡
Bifurcation of the neuronal population dynamics of the modified theta model: transition to macroscopic gamma oscillation
论文作者
论文摘要
抑制性神经元的相互作用在局部田间潜力中产生γ振荡（30--80 Hz），已知与认知和注意力等功能有关。在这项研究中，修改的theta模型被认为是为了研究抑制性神经元的显微镜结构与它们的γ振荡之间的理论关系，在单个神经元对滋补的广泛分布功能下。广义光谱理论研究了模型VLASOV方程的γ振荡的稳定性和分叉。结果表明，随着神经元的连接概率增加，一对广义特征值两次越过虚轴，这意味着仅当连接概率具有合适范围内的值时，才存在稳定的伽马振荡。另一方面，当单个神经元上滋补电流的分布是洛伦兹分布时，弗拉索夫方程将减小为有限的尺寸动力学系统。还原方程的分叉分析与广义光谱理论相同。还证明，神经元种群的数值计算遵循广义谱理论的分析以及还原方程的分叉分析。
Interactions of inhibitory neurons produce gamma oscillations (30--80 Hz) in the local field potential, which is known to be involved in functions such as cognition and attention. In this study, the modified theta model is considered to investigate the theoretical relationship between the microscopic structure of inhibitory neurons and their gamma oscillations under a wide class of distribution functions of tonic currents on individual neurons. The stability and bifurcation of gamma oscillations for the Vlasov equation of the model is investigated by the generalized spectral theory. It is shown that as a connection probability of neurons increases, a pair of generalized eigenvalues crosses the imaginary axis twice, which implies that a stable gamma oscillation exists only when the connection probability has a value within a suitable range. On the other hand, when the distribution of tonic currents on individual neurons is the Lorentzian distribution, the Vlasov equation is reduced to a finite dimensional dynamical system. The bifurcation analyses of the reduced equation exhibit equivalent results with the generalized spectral theory. It is also demonstrated that the numerical computations of neuronal population follow the analyses of the generalized spectral theory as well as the bifurcation analysis of the reduced equation.
