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arXiv · 1005.2699

On the simplest system with retarding switching and 2-point critical set.- Functional Differential Equations

D. A. Filimonov
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Abstract

The system considered in this paper consists of two equations $(k=1,2)$ $\dot x(t)=(-1)^{k-1} (0\le t<\infty),\,k(0)=1,\,x(0)=0,\,x(t)\not\in\{0,1\}(-1\le t<0),$ that change mutually in every instant $t$ for which $x(t-τ)\in\{0,1\}$, where $τ={\rm const}>0$ is given. In this paper the behavior of the solutions is characterized for every $τ\in(4/3, 3/2)$, i. e. in case not covered in \cite{ADM}; as it was noted there, this behavior turned out to be more complex then when $τ\in(3/2,\infty)$. Thus the behavior of the solutions of this system with critical set $K=\{0,1\}$ is characterized for every $τ>0$.

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D. A. Filimonov. 2010-05-15. On the simplest system with retarding switching and 2-point critical set.- Functional Differential Equations. https://arxiv.org/abs/1005.2699

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