论文标题
适用于神经元动力学的强大不稳定性分析
Robust Instability Analysis with Application to Neuronal Dynamics
论文作者
论文摘要
本文涉及对遭受动态不确定性的线性反馈系统的稳健不稳定性分析。这项工作是由一个更具挑战性的问题的基础，并为非线性动力学系统中振荡的持久性提供了一个更具挑战性的问题。我们首先通过引入强大的不稳定性半径（RIR）的概念来形式化SISO LTI系统的问题。我们提供了一种为某种类别的系统计算RIR的方法，并表明它适用于一类二阶系统。该结果应用于用于神经元动力学的Fitzhugh-Nagumo模型，数值模拟确认了有效性，在那里我们适当地护理了平衡点的变化。
This paper is concerned with robust instability analysis of linear feedback systems subject to a dynamic uncertainty. The work is motivated by, and provides a basic foundation for, a more challenging problem of analyzing persistence of oscillations in nonlinear dynamical systems. We first formalize the problem for SISO LTI systems by introducing a notion of the robust instability radius (RIR). We provide a method for calculating the RIR exactly for a certain class of systems and show that it works well for a class of second order systems. This result is applied to the FitzHugh-Nagumo model for neuronal dynamics, and the effectiveness is confirmed by numerical simulations, where we properly care for the change of the equilibrium point.
