Solution manifolds of differential systems with discrete state-dependent delays are almost graphs
Abstract
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 $d_{\kappa}$ are assumed to be continuously differentiable.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.06491
- arXiv:
- arXiv:2208.06491
- Bibcode:
- 2022arXiv220806491K
- Keywords:
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- Mathematics - Dynamical Systems;
- Primary: 34K43;
- 34K19;
- 34K05;
- Secondary: 58D25
- E-Print:
- 16 pages