发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究平面二阶化学反应系统中强非双曲临界点的动力学行为，证明正平衡点情形下仅存在九类几何等价类，并给出各类示例；若平衡点在原点，则十六类均可实现。
AI 中文摘要
在质量作用动力学下，含两种化学物种的化学反应系统的动力学可由右端含多项式的平面自治常微分方程组描述。尽管其在双曲临界点附近的行为已被充分理解，但对于强非双曲临界点（即平衡点附近的线性化为零矩阵）的动力学尚未完全刻画。本文研究了此类化学反应系统的行为。考虑具有正平衡点的二阶化学反应网络，我们证明在一般常微分系统的十六类几何等价类中，仅可能有九类。文中给出了每一类对应的化学反应网络示例。若非双曲平衡点位于原点，则所有十六类几何等价类均可由化学系统实现。
英文摘要
The dynamics of chemical reaction systems with two chemical species can be described (under mass-action kinetics) by planar autonomous systems of ordinary differential equations (ODEs) with right-hand sides containing polynomials. While their behaviour close to hyperbolic critical points is well understood, their dynamics has not been fully characterized for strongly non-hyperbolic critical points, where the linearization close to the equilibrium is given by the zero matrix. In this paper, the behaviour of such chemical reaction systems is investigated. Considering second-order chemical reaction networks with a positive equilibrium point, we show that only nine geometric equivalence classes are possible out of the sixteen classes for general ODE systems. Examples of chemical reaction networks in each class are presented. All sixteen geometric equivalence classes can be realized by chemical systems if the non-hyperbolic equilibrium point is located at the origin.
