Yorke and Wright 3/2-stability theorems from a unified point of view

Pages: 580 - 589, Issue Special, July 2003

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Eduardo Liz - Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, Campus Marcosende, 36280 Vigo, Spain (email)
Victor Tkachenko - Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka str. 3, Kiev, Ukraine (email)
Sergei Trofimchuk - Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (email)

Abstract: We consider a family of scalar delay differential equations $x'(t) = f(t, x_t)$, with a nonlinearity $f$ satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.

Keywords:  3\2 stability condition, global stability, delay differential equations.
Mathematics Subject Classification:  34K20.

Received: September 2002;      Revised: March 2003;      Published: April 2003.