Mackey-Glass type delay differential equations near the boundary of absolute stability

E. Liz; E. Trofimchuk; S. Trofimchuk

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Mackey-Glass type delay differential equations near the boundary of absolute stability

E. Liz·E. Trofimchuk·S. Trofimchuk

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Abstract

For equations $ x'(t) = -x(t) + ζf(x(t-h)), x \in \R, f'(0)= -1, ζ> 0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to zero when both $ζ-1 >0$ and $h(ζ-1)^{1/8}$ are less than some constant (independent on $h,ζ$). This result gives additional insight to the conjecture about the equivalence between local and global asymptotical stabilities in the Mackey-Glass type delay differential equations.

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BibTeX RIS

E. Liz, E. Trofimchuk, S. Trofimchuk. 2002-10-10. Mackey-Glass type delay differential equations near the boundary of absolute stability. https://arxiv.org/abs/math/0111318

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