Covering Relations and Non-autonomous Perturbations of ODEs

Forwards attraction properties in scalar non-autonomous linear dissipative parabolic PDEs. The case of null upper lyapunov exponent

As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product semiflow induced by a family of scalar non-autonomous reaction-diffusion equations which are linear in a neighbourhood of zero and have null upper Lyapunov exponent. Besides, the notion of Li-Yorke chaotic pullback attractor for a process is introduced, and we prove that this chaotic behaviour might occur for almost all the processes. When the problems are addi…

非线性有限维非自治动力系统的精确且最优二次化

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

本文研究非自治、任意维非线性 ODE 的精确最优二次化，提出存在性理论与维度无关算法，并扩展 QBee，以更低维提升和降阶模型学习应用验证优势。

无穷远处动力学中具有法向双曲性质的 ODE 的爆破行为

Blow-up behavior for ODEs with normally hyperbolic nature in dynamics at infinity

本文通过无穷远处动力学描述 ODE 的爆破行为，利用相空间闭嵌入和时间尺度变换将爆破描述转化为地平线上紧轨迹的跟踪性质，并证明具有渐近相位的双曲不变流形可诱导爆破。

Dynamics of quasiconformal fields

A uniqueness theorem is established for autonomous systems of ODEs, $\dot{x}=f(x)$, where $f$ is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every non-critical point of $f$ there passes a unique integral curve.

带非自治线性D算子的中立型泛函微分方程的指数阶

Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator

该研究针对带稳定线性非自治$D$-算子的中立型泛函微分方程，证明卷积算子$\u001b[D\tilde]$的可逆性与一致连续性，引入新的变换指数阶并推导极小集1-覆盖性质，最终将结论应用于一类房室系统的物质量描述。

平面二阶化学反应系统中强非双曲临界点的分类

Classification of strongly non-hyperbolic critical points of planar second-order chemical reaction systems

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。