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Mackey-Glass type delay differential equations near the boundary of absolute stability
For equations with -nonlinearity which has negative Schwarzian derivative and
satisfies for , we prove convergence of all solutions to
zero when both and are less than some constant
(independent on ). 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.Comment: 16 pages, 1 figure, accepted for publication in the Journal of
Mathematical Analysis and Application
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