鲁棒不稳定性分析及其在神经元动力学中的应用
Robust Instability Analysis with Application to Neuronal Dynamics
摘要：
本文研究了具有动态不确定性的线性反馈系统的鲁棒不稳定性分析。这项工作的动机，并提供了一个基本的基础，一个更具挑战性的问题，分析非线性动力系统的持续振荡。我们首先通过引入鲁棒不稳定半径（RIR）的概念，将SISO LTI系统的问题形式化。我们提供了一种方法来计算的RIR准确地为某一类系统，并表明，它适用于一类二阶系统。这一结果被应用到FitzHugh-Nagumo模型的神经动力学，并通过数值模拟，我们适当地照顾平衡点的变化的有效性得到证实。
英文摘要：
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.
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