报告题目：Jacobi stability analysis for systems of ODEs using symbolic computation

报告人：黄博副教授，北京航空航天大学

报告时间：2024年11月5日（周二）17:00-18:00

报告地点：22-214

报告摘要：The classical theory of Kosambi–Cartan–Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been investigated more recently using geometrical concepts and tools. It turns out that the existing work on the Jacobi stability analysis remains theoretical and the problem of algorithmic and symbolic treatment of Jacobi stability analysis has yet to be addressed. In this talk, we initiate our study on the problem for a class of ODE systems of arbitrary dimension and propose two algorithmic schemes using symbolic computation to check whether a nonlinear dynamical system may exhibit Jacobi stability. The first scheme, based on the construction of the complex root structure of a characteristic polynomial and on the method of quantifier elimination, is capable of detecting the existence of the Jacobi stability of the given dynamical system. The second algorithmic scheme exploits the method of semi-algebraic system solving and allows one to determine conditions on the parameters for a given dynamical system to have a prescribed number of Jacobi stable fixed points. Several examples are presented to demonstrate the effectiveness of the proposed algorithmic schemes. This talk is based on a joint work with Dongming Wang and Jing Yang.

报告人简介：黄博，北京航空航天大学数学科学学院副教授，硕士生导师。2021年博士毕业于北京航空航天大学，导师是王东明教授，2018年9月-2020年9月在纽约大学科朗数学研究所访学。主要研究方向包括计算机数学、动力系统定性分析。在Bull. Sci. Math.、J. Symb. Comput.等期刊和ISSAC等国际会议上发表论文20余篇。现主持一项国家自然科学基金青年基金项目，参与国家自然科学基金重点项目、国家重点研发计划等项目。