Solution manifolds of differential systems with discrete state-dependent delays are almost graphs

2022/08/12 by Krisztin, Tibor, Walther, Hans-Otto
#34K05 #34K19 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 34K43 #Secondary: 58D25

paper · doi:10.48550/arxiv.2208.06491

Abstract

We show that for a system x'(t)=g(x(t-d₁(Lx_t)),…,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 C¹([-r,0],ℝⁿ). The map L is continuous and linear from C([-r,0],ℝⁿ) onto a finite-dimensional vectorspace, and g as well as the delay functions d_κ are assumed to be continuously differentiable.

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