论文标题
具有离散状态依赖性延迟的微分系统的解歧管几乎是图形
Solution manifolds of differential systems with discrete state-dependent delays are almost graphs
论文作者
论文摘要
我们表明，对于系统$$ x'（t）= g（x（x（t-d_1（lx_t））），\ dots，x（t-d_k（lx_t）））$ n $ n $微分方程的$ n $ dinatial方程$ k $ k $ k $ ntative contentent依赖状态依赖性延迟该解决方案流形，在哪个解决方案运算符上，在哪个封闭的subspace上是一个简单的图形，是一个简单的图形，是一个封闭的子台面。 $ c^1（[ - r，0]，\ mathbb {r}^n）$。地图$ l $是连续的，是$ c（[ - r，0]，\ mathbb {r}^n）$在有限维矢量空间和$ g $以及延迟功能$d_κ$的线性线性线性的。
We show that for a system $$ x'(t)=g(x(t-d_1(Lx_t)),\dots,x(t-d_k(Lx_t))) $$ of $n$ differential equations with $k$ discrete state-dependent delays the solution manifold, on which solution operators are differentiable, is nearly as simple as a graph over a closed subspace in $C^1([-r,0],\mathbb{R}^n)$. The map $L$ is continuous and linear from $C([-r,0],\mathbb{R}^n)$ onto a finite-dimensional vectorspace, and $g$ as well as the delay functions $d_κ$ are assumed to be continuously differentiable.
